It would be hard (and probably overkill) to try to provide anything besides casting, multicasting and broadcasting of generic messages for real-time multiplayer games.
You could even make it more generic by creating only simple key-value (string-JSON) room storage behind websocket service (with 3with operations like: set, get, observe
- set(key, value)
- get(key)
- observe(key)
- maybe something like setReadOnly(key, bool)
- or more sophisticated permissions API
- maybe API for operations on arrays
It would be easy to use it as a broadcast by observing the same key ("/msg/broadcast") in each client. With API like that you can even have multiple broadcast channels (keys like "/event/broadcast" and "/chat/broadcast"). It could be also used for direct communication and for storage of game-state information (available for players that join the room during the match).
BTW: You can look at Google Play Game Services. They have (among other things) REST API for turn-based matches.