We just wrote a medium post describing our companion app approach to this issue.
To answer your question, the IC as it is right now might be efficient enough to host the web services of a multiplayer game but would certainly not meet the latency requirement for any real-time interaction game scenario. What you could do is either use a hybrid model where only NFTs and, generally, persistent data is stored on the IC or use an extended version of our WebRTC approach or the WebSockets approach that psychedelic has put forth recently.