Game theory needs both players to be making rational choices under the same ruleset to work.
Certain game theory scenarios require both parties to be game theorists to work, I'd contend. It's perfectly possible to extend the initial, streamlined versions of these scenarios into larger, more complex ones that account for more external factors. In fact, I would even go so far as to say that figuring out how to apply those toy scenarios to complex situations with people who are neither legible nor mathematically simple is the actual meat and potatoes of game theory.
All this to say, don't throw out the baby with the bathwater here. Yes, even though Orochimaru is particularly logical he's still far from an idealized game theory agent, but that doesn't mean that game theory logic can't be applied to him. If we think we can approximate the ways in which he differs from an idealized game theory agent, it should be possible to construct a variant game theory scenario for his particular case.
On the other side of the coin, as it pertains to our deadman's switches, it is genuinely a question to be asked whether the value tradeoff is worth it. A deadman switch invariably trades off some % risk that it'll activate against some % risk of the thing you're trying to deter. We want to deter Orochimaru betraying us, and we're trading off part of the world's fighting chance against the Akatsuki. Just looking at it that way, the stakes are high enough that the value could point either way. The amount of deterrence we expect, versus the risk of activation we expect, weighted by the severity of each fail-state, ends up being a genuinely non-trivial equation.
The more you think Orochimaru is likely by default to betray us, the more valuable such a deterrence would seem. The less effective you think such a deadman's switch would be on Orochimaru (or rather, the assertion by Hazou that such a deadman's switch exists), the less valuable such a deterrence would seem. Depending on your model of Orochimaru it could make a lot of sense or no sense at all. If he's treacherous but reasonable, the deterrence is incredibly valuable. If he's untreacherous to begin with, it's pointless risk. If he's treacherous and unreasonable, it'd trigger and only make things worse. The game theory can still be applied, we just also have to debate these extra variables.