It seems that most of pure math research was mainly a form of entertainment for very smart people. Like playing professional chess perhaps, or playing a difficult puzzle game.

Sure, sometimes they accidentally also developed something slightly useful (e.g. Haskell uses some concepts from category theory), but in terms of usefulness the questions are: 1. How useful were this applications it relative to the effort that went into pure math research, in terms of return of investment? 2. Could the useful math also have been purposefully invented by applied mathematicians when an actual need for it arose?