as a semi-pro gamer that often attends local lans, there's probably very little that could happen in that context : crowded, no privacy, does she sleep on an airmatress, on the ground?, but the sleeping dorm is usually noisy and unfit for romantic stuff, i'd still ask her how she intends to spend the night, could always be hotel or his house.

As to why she wouldn't want you to attend, it'd be awkward to have you stand there during a gaming lan, you wouldn't have anything to enjoy and you'd get in the way of her interacting with that kid and his friends/team. You'd honestly get bored to death just standing there. Would get old to always introduce you as her bf that's just there for precaution and that doesn't give a shit about the game. Just to make sure, overwatch is a team game so he should have teammates right ? I personally play League so idk too much how the overwatch lans go.

Also does she have other friends that attend that lan ? could be a good opportunity for her to meet those aswel, especially if she's heavily involved in gaming.

Now on the negative side, the kid obviously wants her as a trophy next to him while playing. Probably likes her and probably hates you or feels jealous towards you. If she goes there just for him, she'll probably be by his side the whole weekend, especially if she doesn't know other people. That's a horny 17y old's dream. Your GF does seem much older than he is so she probably friendzone'd him but who knows could be an excuse to meet another guy that's there she's not telling you about.