do you do rate limiting, how do you protect your websocket?
I think that mainly depends on the load you expect. I mean, even the way it exists now in my sample code it could probably handle a couple hundred to thousand new games per minute without problem on a small VPS. The server component only helps set up the p2p connections, there is no real work involved.
So unless you're building something where you're literally setting up tens of thousands of new games per minute I wouldn't worry. Don't underestimate the scalability of a single executable on a cheap server. Spend your time/money on more important things.