It's not very tangible like "oh that's just like a skewer tactic in chess!", it's more a general ability to think ahead and enumerate various likely scenarios, and ways of deciding what to do. Chess is not just pure pattern recognition. It's also a game of decisions, understanding what your opponent is trying to do, swallowing your own pride, etc.
You can play chess in an almost poker type way, playing risky lines betting that your opponent won't find a tricky refutation. It seems like the board state(and clock) is all there is, but that is far from the truth.
One of the biggest challenges for learning chess players is to learn to consider your opponent's plans and factoring it into your own. This sounds obvious, but from my experience tutoring kids it's very much not the natural state of things. The natural thing is to only consider what you want to do. Which doesn't work if the opponent's plan is quicker. Then you need to find a new idea. Even if you're just a few moves away from completing yours. There's a mental discipline to avoiding the sunk cost fallacy there that can easily be worth a few hundred rating points.
Now, most of the research on transfer of chess skills has focused on things like IQ and working memory, and found no meaningful transfer. But there's a lot more to chess(or any other skill) than that. I'm not convinced this is adequately expored by the field of psychology at all.
I regularly beat people at simpler strategy games even though they're the ones teaching me the rules of the game.
You could argue I'm just naturally good at strategy games, and that's why I play chess. And that must be at least partially the reason. But it's my intuition that some of these more abstract game decision making, opponent modelling, etc skills do transfer(I am biased though, obviously). But that's a lot harder to research than doing an IQ test and a short term recall test.