I think you're right, had the AI (like the second game) had the incentive to maximize the well being of the cooperating actors, rather than itself, the outcome would be different.

But if advanced AI is being developed in a capitalist economy by independent actors, it seems most likely the incentives will be anything other than optimizing the output for the individual outcome.

If that AI finds a way to "hurt" the other actor, there could be some major boat load of unintended consequences.