Yes people have been trying to make chess "AI" since the very beginning of the computer. A chess engine is an obvious thing to build with a computer because the rules of chess are uniquely suited to automation: there's enough possible moves per turn to make calculation difficult for humans, but not so many that it's difficult for computers too (as with Go).
Early AI researchers did try to solve other problems, they just generally failed miserably.
Early AI researchers did try to solve other problems, they just generally failed miserably.