Right, "blockchain" just means "chained cryptographically-dependent messages", in this case the mini-blockchain just uses proof-of-intent AKA signatures. No matter what, you need signatures from players on the state of the table up and including their decision, so theoretically at minimum you need a message of the form "sig_a(state_n, sig_b(state_n-1, sig_c(state_n-2, ...)))" initialized by the host and signed as it passes around the table, which is accepted as a transaction into the main chain. Hosts should have some freedom about what the message has to look like as long as players sign off on it (like, "host is allowed to kick players after just 15 seconds" or something).