Basically users can interact by playing basketball games against each other or by trading players. This sort of interactions are handled with something similar to a TCP handshake, since we must ensure that we end up with a consistent state at the end (e.g. players are traded consistently).
Because of this, it is not easy to have 'real-time' interactions: for example, when challenging each other, players only agree on the initial conditions of the game, which then is simulated independently (and deterministically) on both clients.
raft is too non-deterministic. Something like paxos is probably more appropriate; the write-once property is exactly what you want here, and it is deterministic.
Talking about blockchains is fine, pretending they are somewhat apt at solving a problem that isn't money laundering is what will get you frowned upon.