And given that, a lawyer could argue that paying to play on (or even donating to) a private server is contributory copyright infringement. I don't know if that has been tested in court.
You mean Diablo and Starcraft? They do cost money, yet still require access to Blizzard servers, and running on separate servers is a T&C violation, which the DoJ considers a violation of the CFAA.
https://arstechnica.com/gaming/2010/08/the-88-million-server...
And given that, a lawyer could argue that paying to play on (or even donating to) a private server is contributory copyright infringement. I don't know if that has been tested in court.
https://en.wikipedia.org/wiki/Contributory_copyright_infring...
But oftentimes you can get away with it; few game companies go after small private servers.