I don't think there's a meaningful difference between the Pentium and the 80386 except speed. You might have to change the compiler options a bit.
And, with more work, that's true of computers in general; they can all do the same computations once you somehow wire up enough memory: https://dmitry.gr/?r=05.Projects&proj=35.%20Linux4004
I understand about Turing machines.
For chess though, there are time constraints. The 386 is a lot slower. Is it fast enough?