Yes, the (very nice) game you described gives a separation between classical and quantum mechanics. However, there is a strategy in real quantum mechanics which

Yes, the (very nice) game you described gives a separation between classical and quantum mechanics. However, there is a strategy in real quantum mechanics which also achieves a 100% winrate for the players (you just need higher dimensional Hilbert spaces for each player). Instead of preparing |+++> + |–-->, you prepare the state (|+++>|x> + |–-->|x>) Here, |x> = |000>-|011>-|101>-|110>, and one qubit is sent to each player. That is, you give each of Alice, Bob and Charlie an extra qubit. They can now measure in the computational basis on both qubits. And in the betrayal round two of the players can perform the orthogonal transformation id \otimes J, (controlled on having |->) where J = {{0,-1},{1,0}}. You can check that whenever exactly two players perform this operation on their systems you get back the state (|+++>-|--->)|x>, and thus your previous strategy works. This simulation strategy for any full multipartite causal structure is described in arXiv:0810.1923. What OP has shown (roughly) is that three players connected as in A <-> B <-> C (where <-> is some shared randomness or quantum state) then this simulation breaks, and indeed there is a gap between what you can achieve in real and complex quantum mechanics.