This is a very weird one to handle.
From the videos, he is indeed crouching before he fires but he isn't following through with the next part which makes it a crouch glitch i.e firing 1 shot whether it be from shotgun or m4 then, sprinting+switching weps.
For example the first video you posted, he crouches at 0:11 and then stands back up and fires the M4 for 3-4 shots then sprints away (which isn't a crouch glitch at this point)
Then around 0:24 there is another moment where he crouches very momentarily but again like before, he doesn't follow through with a crouch glitch he fires about 8-10 shots.
Similarly in the latest video at downtown, at 0:03 he crouches and then jumps backwards.
Basically, to sum everything up, their isn't any crouch glitching here that I can see, he's just crouching and firing a weapon then either holding position or jumping. Remember, crouch glitching occurs when you fire the weapon very quickly (1 time usually) as you crouch then sprint, change weapons and run.
I don't know what his thinking is behind this, is he somehow trying to duck and avoid the first shot? or is it possible to do a ghost shot by doing this?