I think what he means is;
Alice and Bob receive a destination.
Alice and Bob must both reach that destination utilizing the same path.
If there is a random element(ie they walk different paths), then it will not work.
does four deuces win against a straight flush?
does three of a kind beat two pairs
like that, as long as each node can determine who has which cards from the events and has a deterministic way of determining the winner, theoretically it can be done.
however, if the game has something like: "in the event of a tie, flip a coin", then this tie break coin flip needs to be encoded in the group shuffled random numbers and it cannot be determined on a node by node basis