If you run during the fall and take damage from the fall, then your stamina will be replenished.

The question is, can this be considered a glitch?

No, is this suppose to happen, to "replenished" your stamina.

I just find it weird that when you take damage you regain stamina.

Think of it like adrenaline "fight or flight" response!

Well, probably, since you can’t avoid it, when you fall, shouldn’t think of it as a glitch

This is normal and me and the person I run with call it "damage boost", it's an intended game mechanic and not a glitch. Provoking it on purpose is just clever use of the games mechanics to get a speed boost.