Golf is the clear example of being a noun and verb, because you can golf, and play golf. Just like games.
To golf is the exception, not the rule for all English. As for the verb to game, as language changes, maybe it's fine that term is applied to video games as well as gambling, but the problem most people have is the connotations it brings. How many times have you heard the crew put on their XXXtreme gamerz voices on the Bombcast/Hotspot? In mainstream media, video games are often seen as a kids thing or a hardcore nerd thing.
I agree with mshaw006, it would be good to get away from labels but the trouble is, it's a lot easier to say "Brad is gay" rather than "Brad has a propensity towards loving men." Even now, it's hard not to be influenced by words like 'gay' even though we are all aware that someone being attracted to a certain gender or lack of gender doesn't tell you anything about that person. The same goes for any noun used to describe people, which is the whole problem.
I'm not a straight junglist gamer. I like women, I like Drumfunk and I like playing games but none of those tell you who I am.