I agree about zoning and permits, in general you shouldn't need too much, nothing different than if you were doing remodeling inside your house. However yes anything electrical usually requires a permit. But that does vary depending on your local govt so you have to check your codes. Around here -any- electrical work in the home requires a permit. However, you could do it yourself if you wanted to (city will come and inspect your work). I know in other places, it is also a requirement that only a licensed electrician can touch anything electrical.
The one thing they do look for is any modification that could possibly turn that garage into a living space, that is, a bedroom. That is where you have to be careful. I think this would be triggered by adding plumbing or a bathroom, which it doesn't sound like you want to do. You gotta check your local codes. Once it becomes defined as a bedroom or living space, then there will be a bunch more codes and rules to comply with, including such things as egress (in case of fire) which includes placement and size of windows and such.
Sure its gonna cost you. But it all depends how bad you want it and if you can afford it. I have seen lots of threads in the game room forum that include spending a lot more than this just on the game room structure. The pins demand it!