Played at high level, sports don't really increase fitness beyond a point, they increase your ability to play in your role. Football players shorten their lives in many ways, and no, not all of them are related to head banging injuries. Is that fitness? For a quarterback, likely. But plenty of the team is about fulfilling a role. Sumo wrestlers don't live long either- sustaining that much muscle (and of course the famous fat) is hard for any body.
Played at a casual level, of course sports offer benefits. Play football with your other sedentary buddies and you will all increase health.
Played at a high level, e-sports don't really increase cognition beyond a point, they increase your ability to play in your role. Starcraft players don't go on to make vast maps in their head, or use their extraordinary decision making skills in some manner, because a role for those explicit cognophysical tricks just doesn't exist outside of video games. Is that intelligence?
Played at a casual level, of course e-sports offer other benefits. Play starcraft with your other non-computer aware buddies and you will all get better at computers, reaction time, decision making, planning ability, and other facets of cognitive health.