There are these venues in my neighborhood with computers and sometimes consoles in which kids play video games especially team video games such as Counter Strike. We call these venues gamenets although I can't get google hits on it. I thought maybe the closest word would be video arcade but it seems a video arcade includes much more games than just video games. What's the word for such venues?
Internet café, or cybercafé, comes to mind when reading your description.
While these are not exclusively for playing video games, it is one of the main activities happening there.
Well, I'm not certain what it could really be as I'm not a native speaker but I often come across the term "computer club" where people surf the web, work, play games (single player or multiplayer), or do whatever else they want.