One of the problems you may have in keeping the game room is that you aren't focusing on the desired outcomes for the gaming room.
Many library gaming programs struggle because they focus first on the gaming activity, instead of starting with the desired outcomes. If library gaming programs starts with "first-person shooters are cool, so we should have those," then it will be a problem to justify the gaming.
Deciding on the difference that gaming should make in the library (that falls in line with the library mission), then developing the gaming programs to make that difference, and then assessing the programs to demonstrate the difference the program made makes it a justifiable gaming program.
So, the questions I would ask:
- What differences in the lives of the users does the gaming room make, and how does that fit within the goals and mission of the library?
- How do the choices made in developing the gaming room lead toward making those differences, and why are those choices the best way to make those differences?
- Can you assess the users to see if these differences are being made?
If you have this data, then it is much easier to argue why the gaming room should exist.