I'd say it has to go between Valve, Bungie and ID, although I could also see treyarch
Valve for obvious reasons. Counterstrike is still a juggernaut after all those years.
ID has the best feeling arena style shooters in the business and both recent DOOM games are of very high quality in all aspects.
Bungie deserves this spot even though I really do not like Destiny. But the gunplay is always snappy and smooth.
Treyarch is a weird one, because I personally do not like Call of Duty for a whole lot of reasons. But you just can't argue with their gunplay. The aiming is the smoothest in the business. I believe (apart from the insane magnetism/AA) every shooter should just copy how insanely smooth aiming in COD feels (looking at you 343)
Honorable mentions to Respawn. I don't think I've played a game of them where the gunplay wasn't insanely smooth and snappy.