One thing I am genuinely surprised by quickly reading and considering my experience in retro FPS is that most of them seem to be based around using movement for defense. While some retro FPS use cover to some degree, generally cover isn't as much of a focus like in modern shooters (thought cover is a mechanic in GRIM and dodging isn't). Instead the focus is usually on dodging projectiles (be it Imp fireballs in Doom or Cultist dynamite in Blood). Currently movement is purely tactical and about cover and sightlines.
I'm not sure how it could be implemented. One way I can think of is adding a Dodge mechanic, where you can end your turn with an un-used action. If you get attacked before your next turn, you can spend that action to Dodge it, giving enemy a disadvantage on that attack roll. (One action - one attack disadvantage) However if you won't get attacked the unused actions are wasted.
One advantage of setting it up like that is true to spirit of Quakes and Dooms, the Speed stat would become as valuable defensive tool as Armor (because it would give you free actions to burn).
I'm curious what you think!