Is the download file the same as the scrollable pdf? I looked over the pdf and did not see any archetypes. Maybe I missed them.
I am not aware of a Fighting style at second level being part of the standard fighter.
I would like to see a spell-less support class but why not build a solid support class and then put Warlord and Bard in there as subclasses? That seems like the way 5 is doing it and it should save you the work of building your spell-less Bard.
At level 12, Warning Shout reduces ~22 points of damage to someone every time you use a reaction. (reactionary action = reaction). That is pretty significant healing. The long rest cooldown is a little disjointed. "Sorry man, I couldn't warn you this time because I warned you last encounter."
Combat Medic is a common mantra for Warlord builds but it is something that never made sense to me. In my mind a combat medic is less of an authority/leadership/enabler focus and more of a run through bullets to get the fallen kinda guy.
Fantasy Commando and Green Berets is a valid playstyle but I think a spell-less support class would get more play if it was designed with the same space as the cleric but not tied to military application like the typical Warlord draft. That way, players that fight lots can have a support class focused on combat or a support class that has a clear advantage exploring, or one that is a socialite. There are players that play clerics to support their mates, but begrudgingly because they don't want the religion factor or spells.
I would make the abilities "warlord level".
Warning shout: should be per short rest, putting it more on par with second wind. Also probably add "if this reduces damage to 0, it's a miss".
That's what I thought, but it shows up as a first level and a second level feature. Does this Warlord have two fighting styles by level two?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.