I never played 1E, but I played AD&D 2E for close to a decade. As I understand it, the systems are similar mechanically.
I don't think it felt like AD&D.
In AD&D you could count on magic working. You can't have a utility spell fail when it's absolutely necessary for pulling off the plan.
In AD&D races/ancestries matter. (Darkvision, magic resistance, ability score adjustments.) They basically do nothing in Shadowdark.
In AD&D you can get skills, non-weapon proficiencies, weapon expertise - if you want to use those options.
In AD&D your ability score bonuses weren't as impactful as they are in Shadowdark, which was seemingly designed for a different method of generation.
In AD&D the monsters had more that a paragraph of detail, including ecology, background information, treasure charts, and a variety of mechanics.
In AD&D you could customize your thief with different percentages in thief skills, your cleric could be different depending on spheres, and your wizard could specialize in schools of magic. Druids, rangers, paladins, and bards gave interesting options as well.
I'd definitely prefer a AD&D-inspired game to Shadowdark. Sadly, the OSR is stuck on B/X.
In AD&D you can mostly count on your utility spells working. Other spells usually allow a saving throw. At higher levels enemy saving throws get really good, not to mention magic resistance! The tradeoff you get for utility spells not always working in Shadowdark is you get more spells in general (three spells for a 1st level Wizard in SD as opposed to one for a 1st level M-U in AD&D), even before we account for the chance to cast them multiple times if you roll well.
Ancestries don't do "Basically nothing" in SD. Mechanically they give at least one special ability and they determine starting languages. They don't give ability score bonuses, which I rather like because it makes them less of a tool for min-maxing, although Dwarf, Elf, and Half Orc do each give a simple numerical bonus (to HP or particular key checks) so you can do that a little. SD is definitely a lighter rules-set than AD&D. Whether a given gamer prefers lots of mechanical detail or less is a matter of taste. I haven't run SD for a long enough period to know whether it's too light for long-term play for my tastes, but I'm certainly hearing other folks report that it works fine for them. Mike Shea of Sly Flourish recently finished a year-long campaign, for example.
Skills, non-weapon proficiencies, and monster details are definitely more of that rules light vs rules detail preference. Kelsey clearly focuses on making the rules quick to read and reference and letting the DM fill in most of the fluff (or get that from supplements). Shadowdark has Backgrounds which function very much like the Secondary Skill system from 1E AD&D, though more generous. Classes also specifically have skills in the form of abilities which give advantage on particular kinds of checks, like Thievery gives for five different ones for Thieves.
AD&D ability scores are funny. At the extreme ends you can get big bonuses. Gary tells us in the '78 PH that it's usually essential to a character's survival to have no fewer than two scores of 15 or better. Dex gives a big +4 at 18 and starts giving benefits at a mere 13. But for even a +1 to Damage you need at least a 16 Strength. The huge benefits of an 18/00 are reserved for the very lucky and the cheaters.

A 16 Intelligence will only give a Magic-User a 65% chance to learn a desired spell! Gary was clearly expecting people to use much more generous ability rolling schemes than OD&D's 3d6 down the line. B/X starts bonuses at 13, which is just within one Standard Deviation from the mean of 10.5 on a 3d6 bell curve, so the B/X and BECMI bonus scheme is much better fit to the math of 3d6. Shadowdark letting bonuses start at 12 and ramp up every 2 points like WotC D&D is also designed to work well with the 3d6. Kelsey gives the optional rule of re-rolling if you don't have at least one score of 14 or better, which does help ensure competence. I prefer the "flip/mirror" house rule, which I think I described in my first contribution to the thread, which doesn't guarantee a 14 but does guarantee that you never have a set below average on the whole and that you never need to re-roll.
Most of the character customization you're talking about in AD&D sounds like 2E rather than 1E. Shadowdark is definitely deliberately built to reduce the character build game. Characters within a class can certainly be different from one another by rolling different Talents and making different choices- which weapons to have Mastery with for Fighters, for example, which abilities to focus on for Thieves, which spells to pick and which to get Advantage with for casters, etc.
It's not "in-fiction" as OSR titles are not (in my opinion) fiction-first games. Instead, they reward clever planning and the use of resources to navigate challenges.
If all magic must work the same in Shadowdark, then it must all be reliable, else the system fails to reward clever planning, leaving the whole venture to a coin flip. The hallmark of the OSR is that clever planning needs to be rewarded, that player agency is a GM virtue. As long as magic works as it does in Shadowdark, this cannot be true.
How many times has a plan hinged on the ability to turn a character invisible or give the ability to fly/levitate/spider climb. After the plan is forged with deliberation, a 50/50 chance can make the spellcaster unable to use the magic for 24 hours. In my case, I had to vacate a crumbling tower and had the foresight to take feather fall. I should be safe, right? Nope. 50/50 chance of spell failure. Nothing you can do - you're dead from impact.
It's not really 50/50. With the min 14 rule in place a human or elf caster usually starts with a +3 or better to casting rolls, which means a 60% baseline for their three spells for a Wizard or two spells for a Priest. Having more spells means more chances to succeed. Getting Advantage on a spell of your choice is one of the most common talent rolls for Wizards, and it comes automatically with Magic Missile. At higher levels chances get better, especially with the lower tier spells. On the Wizard talent chart 30 out of 36 possible rolls improve your chances to cast (the others give you a free magic item or an additional spell - both of which give you more power and more chances to use magic).
And Luck Tokens are a core rule, which speak to the OSR philosophy of rewarding planning and resource management. Giving Advantage to a key casting roll makes it much more reliable. It's not a 100% guarantee, but I don't think your premise is valid that rolling for magic eliminates player agency or the value of planning.
Mike Shea reports that at higher levels once PCs accumulate bigger bonuses, between those bonuses, spells which have Advantage, and luck tokens, his experience was that key spells become very reliable. And of course every time you succeed you also have the spell available to cast again...