That's the thing: Core War matches last a finite time (after which the match is judged a tie). So you have a finite memory space, finite time, and a finite number of match combinations. And for predetermined constant N, the bounded halting problem ("does the program halt within N steps") is in NP.

For the nano hill[1], the constants are: each warrior has a max of five lines of code, core size is 80 instructions, and a match lasts a maximum of 800 cycles.

If N = 1, it's clear that the best you can do is drop a bomb at a fixed location and hope you hit. So that is mostly a tie. For N=2, it's probably still not possible to do anything useful. With N = 10, perhaps a quickscan is possible. N = 800 -- who knows?

[1] https://corewar.co.uk/nano.htm