You don't need mind games to play chess. You just need to memorize thousands of pages of book openings / end game scenarios and play thousands of matches against rated opponents until the middle game becomes second nature.
Or you can just do what I do, which is to learn some fundamental principles and how to apply the principles to various positions. I generally only think 1 - 2 moves ahead in chess unless there is an obvious combination, and I'm pretty decent.
Regardless, there is little transference between chess and Melee skills. I am very intelligent and good at chess, but I can't transfer many of these skills / attributes to Melee, especially regarding "mind games" which rely substantially more on reaction time than on strategy. Interestingly enough, however, my tech skill actually correlates strongly with intelligence, and not, I think, with any special amount of dexterity. When I started playing Melee I thought carefully about how to hold the controller to maximize technical ability (a specialized version of clawing). It took me a while to get it right and to get used to it but now I can do things that many players, who probably have more dexterity than I do, cannot. Moreover, whenever I try to learn a new technique I think carefully about the optimum way to do it. For instance, in order to do shine-turned platform wavelands I just noticed that if you space the shine a set distance from the platform the timing is identical to shine-turned wavedashes. The timing for shine ledgedashing is also the same. But this all depends on how you waveshine--you really need to do it with the exact same technique every time, letting the stick revert to neutral between the shine and wavedash, and start the wavedash the exact same (within a couple frames anyway) delay after the shine. And I can do this consistently with little effort because I thought about how to hold the controller and do every technique before I learned them. This is just one example, but hopefully you see the point.
Anyway. Intelligence or chess-related skills are not really related to mind-games or "strategy" (I'm using scare quotes because the strategy in Melee is very shallow) but can potentially play an important role in how you learn things, how you practice, which characters to learn, how to counterpick well, etc., all of which are actually outside any given match.
, btw conker is the sig maker lol
