There are some basics, like thinking about your goal, thinking about your opponent's goal. A newish player will start realizing that they can advance their goal and foil their opponent's goal. A few shades beyond simply missing basic moves, and actively exploiting pins, forks, and skewers. That level, competent but far from elite, i think generalizes reasonably well.

I think you're at a much more specialized level. You need to see many moves ahead, and predict your opponent effectively. That won't generalize so well, because it's purely focused on the rules of chess.

Would you consider mathematics to help you in everyday life? I'm wondering because I know some people who argue that it doesn't, while I argue that it does. We might be confronted to a similar issue here?

Yes, probability is helpful to me in everyday life.