By the time they were trying to defeat the world champion, they didn't really think of it as an AI project any more. They often used the term "expert system", which had a much narrower scope. It had become a challenge unto itself, but they didn't expect it to lead to any kind of generalized intelligence.

It came rather out of nowhere when neural-net-type engines suddenly swept back into dominance. Even after becoming the world chess champion, nobody expected Go to be solved any time soon.

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.

There were chess playing engines circa 1980 on 8 bit micros (e.g. Sargon) that were a good match for ‘average’ players, Deep Blue beat Kasparov in 1997 with a large amount of custom hardware, Stockfish has been very strong on a powerful but ordinary PC since 2008 or so.