This is more a of a loaded community question, than an outright idea.

CSGO or Modern Warfare, though you've got 120 degree view around you and head-tracking, but you control your crosshair with the mouse for fast-paced competitive reasons. Motion sickness is a thing but lets be real here, if it can be done someone's gonna do it right. Does anyone know of any examples of something like this out there?

I'm getting motion-sick just by reading that description.

Did you check the VR tag? There's a few first person shooters in the first page of results (among a whole bunch of adult games, so maybe don't try this at work).