For footnote #1, it may be useful to give a couple of examples. When both programs are making decisions based on the others source code, it is pretty close to the undecidable situation, but it depends on the game.

When the game is Rock-Paper-Scissors (or parity), the programs have contradictory goals and are pretty much the textbook example of noncomputable.

But if the game is the Prisoner's Dilemma (or the Coordination Game), they are trying to cooperate to land on (C,C), so they want to be decidable.