"you win and I go to jail forever / I win and you die" actually literally is a zero-sum a game. People fight/support wars over even completely unrealistic fears that they might one day lose even a bit of their freedom.
Maybe you mean that deciding not to voluntarily lose that zero-sum game makes someone a sociopath. And, tbh, in that situation, I would rather surrender than kill (for a lot of reasons, both moral and practical). However, I also wouldn't call someone a sociopath for deciding to kill in order to avoid a life sentence. "Live Free or Die" is literally the motto of the state of New Hampshire.
If I were about to arrest someone who knew they were going to jail for life, I would go into that situation expecting a life-and-death struggle. Even if that person were a completely balanced and mentally healthy person. Anything less seems a bit naive.