Video games gave me a common ground upon which to approach and communicate with people who I may never have otherwise. So yes, they have had a positive effect on my social skills overall.
Nowadays specifically, though, it doesn't play too big a role as the industry has gone one direction while I've gone another. For example when speaking with my college adviser, she mentioned the campus has a gaming club which gathers weekly and that it may help me to ease into things. My initial reaction 15 years ago would have been "Awesome!" However on that day, I thought to myself "No thanks. I'm not big on shooters, sports, and racing."