How can a hypothesis be tested on video games cause bullying

You would likely need different games and maybe a non-game activity. My working hypothesis is that adding message boards to more competitive online games is what increases game-related bullying. So maybe you should have games with and without message boards, a single-play game, and a non-game activity. With the online games, you could have remote monitors and a team to monitor the game and how the person treats the other players. But if you want to test between games, then you may need a post-session survey, and also have your team to record any behavioral differences between sessions, rude behavior at the facility outside of the games, etc.

You could use a highly competitive game of a personal nature (like certain games that appeal to girls) and a non-competitive game with a message board like Woozworld. Violent games would not be a good measure for cyberbullying, since everyone knows such behavior is part of the game and expects to receive it. But they might be a good measure in whether they exacerbate real world bullying after months of play or not.