Per the discussion in the comments of the question, I think the only recourse is to make a requirement in the Terms of Service for accessing the server.
The license of the server can't impose additional restrictions on the client as they are another separate piece of software. Even if it could, the AGPL provides for a way of removing those restrictions.
All other non-permissive additional terms are considered "further restrictions" within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term.
Without an incentive to keep said term, it would be pretty hard to enforce.
Making it a requirement in the Terms of Service comes with its own baggage. You can't keep someone from creating a proprietary custom client and using it on their own server.
At the end of the day, likely most of this won't really matter though. Given that it is a freely licensed game, with a freely licensed "official" client, the chances that someone will not be willing to offer their code under a free license is pretty slim.