In general they look very fun and powerful and for a self-contained, content control environment like a video game they are probably fine, and they look like terrific fun, but are quite likely going to over-shadow the stock subclasses thief, champion, healing domain, and whatever wizard has. In a tabletop environment Shock mage and Battle cleric are tooooo good, they'd overshadow other classes trying to do similar things. On the other hand, Darkweaver and mountaineer are very dependent in fighting in the right kinds of places to do their things, and this will weaken them greatly in a generalized table top. If you aren't' spending 50% of your time in a dungeon or cave system, you're missing out a perhaps too much of what the subclasses provide.
Battle Cleric: This guy does everything an offensive cleric wants; fights with sword, fights with spells, makes others fight well. Perfect option for making a video game cleric be what a player wants them to be. In the table top world, it has too much of "It all". Other domains are good at attack with weapons OR Good at spell slinging OR whatever, this guy just gets everything. Two attacks, fireball, permanent 5ft buff aura. I want this option in a video, I don't want this guy at a gaming table.
Domain spells: A very good list. Perfect for a video game, toooo good for the table top. Since we'll likely only have three domains with Solasta (right?) making one give you a bunch of highly desirable battle spells is pretty much exactly the right call to make. I wouldn't change a thing.
-At the table top you'll outshine every other domain that has a mix of good and weak spells held together by theme. This guys list has the theme of "Every battlespell you should take and also acid arrow"
Divine Fortitude: You might want to change the wording so that this doesn't get confused with being a Channel Divinity (remove the word 'channel' from the description). For a level 1 power, this is fine both for a video game and on the table top.
Decisive strike: Great power for a video game, in the demo this was kind of neat to get off a attack of opportunity and really ruin a spiders day. Level 2 stun (save ends) is a bit early (monks get stunning fist at level 5, and that lasts one round) but in a video game it's a simple, concrete, and super useful effect.
-For a table top version stun should either be down graded or 1 round maximum. (wisdom save or frightened, save ends might be about the right power level)
Herald of Battle: A perfect simple powerful aura balanced by its limited range. It encourages a certain play style. Exactly what you want in a video game. I like it.
-For a table top version...I think its too much. Looking at other level 6 powers. I think +1 attack by itself might be too powerful, and +1 ac is pretty close as well. I'd say +1 damage and saves would be about what you can get away with, and that's pretty decent.
Zealot of Battle: There is a common theme in domains at this level, weapon clerics get +1d8 damage. Two attacks is quite a lot better than that. People really like getting two attacks, so I doubt changing it to +1d8 damage would be popular, but that would be the "Balanced" choice. This is just power creep, and will really improve the clerics combat skills. I can't support this decision, but if you don't listen to me and the final product has two attacks I will not be in anyway sad. I will in fact be happy.
-For the table top, Two attacks is so much better than +1d8 damage that people would take this domain solely for that ability alone, let alone all the other power this domain offers. Perhaps all weapon clerics should have two attacks at level 8 rather than what they're given, but that's not the 5e we live in and this isn't something one domain should have if the others can't.
Godly Might: This is really powerful. Max damage is a huge thing. Its really, really good. It fits the theme of this build really well, but I fear you might be over shadowing other weapon classes at this level. I don't know if we're getting to 17th level in solasta, but if you do these clerics are going to start just killing every thing.
-For a table top game, this is well beyond what should be happening at this level compared to other domains. It averages to something like a +3.5 damage with a d8 or +5.5 with a d12 (just some quick math, I could be off, didn't include crits) on every attack. this needs to be once per round OR activate for 1 minute Or some other limitation. You could probably sneak away with +2 or 3 to all weapon damage, but actually maxing each and every roll just isn't going to be right.
Verdict: I like it a lot for a video game domain. In the environment of the game it gives you a lot of use and gameplay for this character to be useful in, 8 and 17 might be too good, but so what, they'll be a lot of fun.
Darkweaver: I like it on paper, but without knowing how often I'm likely to get above my enemies, it might be a hard sell. Solasta seems to imply that this will happen a bunch, but how often will it really be? Will it be enough.
Spider on the Wall: Fine. exactly what you want from a spider.
-Table top: it overshadows the thief's Second Story Work, perhaps, but that's not a big deal.
Predator: How often will this happen? That is what makes or breaks it. Will the +2 be something in need to work hard to achieve or will it be something that naturally occurs and that I will benefit from a lot? That is what this power will live and die on. I don't know the answer at this time. It might be a little weak. It's possible that making it "You may sneak attack enemies with a ranged weapon if they are lower than even if not granting you advantage or adjacent to ally" would be a better, more alluring version. I just don't know.
-Table top: Probably too situation and for just a +2 damage? It's not going to draw people to the class. I would certainly consider letting height trigger sneak attack for a table top.
Spider fall: Cool idea. Cool ability. Very powerful. Requires set-up. Compare to assassins 3rd level ability Assassinate and this is probably easier to set up. If getting high is reasonably easy to do, then this power will get used a lot and have a huge impact on this class and what it does.
-Table top: Compare this to other 9th level abilities and its pretty far out of line. Most other rogue subclasses get a minor skill bonus or a cute movement ability. This is a murder button. It's a murder button that your DM could accidently never let you use if you tend to fight in level playing fields, or it's a murder button you could hit every turn (cunning disengage, move climb, action spider fall, repeat). If you made it: "when You jump and attack enemy below you, you take no fall damage and may sneak attack if not able to otherwise" that would probably be closer to where it should be.
Ambush Style: Both are neat, and cool for a game. However, when are you going to poison something and have it live for a whole hour? Never. Poison it for a minute.
-Table top: Probably fine I think. I doubt much needs to change, maybe tweak shadowy invisible rules.
Spider Features: Spider-Man, you say? Seems decent, though spider escape should probably clarify how much horizontal distance you might move.
-Table top: Probably fine, actually, gaining both options might be fine given the situational nature of spider escape.
Verdict: I can see how this could be a very fun class to play in a dungeon crawl video game, I'll certainly be considering it. Probably needs some tweaking to make it a broadly appealing table-top choice, though.
Mountaineer: Interesting. A tunnel and shields fighter. Probably great in the game and maybe adaptable to a table top.
Sheild Bash: Cool, great. Tells you what you should be doing and helps you do it. Perfect.
Tunnel Fighter: Okay. You'll probably have better AC than heavy when against a wall, and lower when not. Probably fine.
-table top: your level 1 powers are fine but maybe a little lackluster. Maybe toss another bonus on the tunnel fighter, but you probably don't need to.
Traverse: I actually really like this. It's cool, and positioning abilities are great. Maybe your motion shouldn't provoke opportunity attacks from others so that you can use it better in the thick of a battle.
Shield Charge: Gives you a good reason to shove rather than attack, stunned is powerful, but in a video game I think its a good effect to hand out on something like this.
-Table top: I'd probably reduce the stun to something else, and maybe add some more options than it only be on shoves from shield bash.
Tunnel Home and Advance Tunnel Fighter: They're fine. They support the flavor. They support the mechanics.
Verdict: It's solid, and I think very little would need changing to make it a good, and attractive table-top subclass.
Shock Arcanist: Powerful evocations of blasting things. This is what you want in a video game subclass, something to appeal to the ones who just want to throw fireballs.
Arcane warfare: I really liked this in the demo. An extra scorching ray or magic missle feels real good when it's free. It's worth noting that as a 9th level spell meteor swarm has no written effect if cast at 10th level (Obviously you can change that, but it's something to make sure you attend to).
-Table-top: No. The spell list is too specific, it limits you quite a lot and makes you cast the same spells over and over (I've no problem for a video game, but it's not ideal in a live-play setting), and the effect is too much, you are literally casting every spell one level higher. It leaves every other school in some really sad dust. It'll need a real make-over before it should come near my table.
Arcane Fury: Seems fine
Arcane shock: Comes a bit late, but I can't really see it being appropriate earlier, but has some real impact. I worry that once a long rest is going to give you too few activations though.
-Table-Top: I Think the really overshadows other level 10 schools. I don't see a way to reconcile this and keep the subclass as written.
Magister's Wrath: How many party members are going to be other wizards (or I guess sorcerers)? Zero in many, many cases, and a 14th level ability shouldn't really be making that decision for a party. I don't like it. If it could affect any character somehow, or just another spell caster it would have lots of use to me, but I'm just worried it's going to be really easy to get no use whatsoever from this.
Verdict: I don't like Magisters Wrath, but the rest of the abilities are perfect for a video game zapper mage. I just don't expect it to be a remotely fair thing to bring to the table top looking anything like it does.
So for the most part, I think that these are great for a Video game, and if the other subclasses you make are anything like them I'm going to have a really hard time choosing! They address the most important things you want in class customization in the sort of limited options environment dictated by nature of it being a video game. I think Battle cleric and Shock Arcanist do a good job of distilling what people want out of their classes. I don't think they need to exist outside of the video game. Darkweaver and Mountaineer are fun and I hope they work out well in the types of landscape Solasta will take us to. With a little tuning I think they could be fun at a table as well.