Online playing = greater social skills, that I don't know about.
But there was a pretty convincing TED talk recently about FPS games and some visual perception/processing ability improvements. Significant ones, actually. Not anecdotal, and not simply survey-type statistics, but repeatable lab experiments with measurable effects that lasted beyond the game playing. It was done by a Swiss scientist, but I forget her name and don't recall the name of the TED talk.
She was not, by the way, saying that (1) you should play games all day, nor that (2) it's a better way than other ways (say, for example, sports, which I'm sure must help visual perception as well), etc.
But it wasn't useuless outside of holding a controller, it wasn't only muscle memory, etc.
This coming, by th eway, from someone who pretty mucn never plays FPSes. I much prefer strategy or RPGs (it's all about the story!). And fun, social-ish games to play with other people that are just fun, like the Lego series.