Kolmogorov complexity is just the standard name for a concept that's useful across machine learning, AI, compression, etc. It's not just a definition in some obscure result in complexity theory.

OP was simply saying that, in any general-purpose programming language (where all possible programs are expressible and none are unfairly favored) the solution to problem B will inevitably be longer than problem A. This is quite a bit more precise than just saying "a more complicated problem", and if you have the intuition behind it, there's no reason not to use the term.