Rock-paper-scissors over network, how to protect from cheating server?
If they don't trust the server they sure shouldn't send any money. The "trusted" third party is used to solve the problem of participants who don't trust each other. So by definition, your problem can only be somewhat mitigated, not solved completely.

I'm not sure what you mean by "provably fair". If the server can't prove he cannot cheat, it's not provably fair.

One way to do that is to award the bet to the remaining player if one leaves the game for any reason. Now if the server decides to keep the money by becoming unresponsive, Alice will know not to trust that server in the future, instead of keep losing money to it.

Another is to start communicating with Bob before the game begins and agree on a server at random. Now the probability of a server ripping off Alice is equal to the probability of Bob colluding with that server.

Lastly rock-paper-scissors doesn't depend on some input from the server, so the server can't prove fairness ahead of time.