Because these endeavors all lead to novel tools and learnings that are at times applicable in surprising ways to help solve "whatever important problem."
For example, number theory, on its face, seems completely useless, and since 1800 BCE, years were "wasted" by scholars toying with useless factoring problems...
...until we got RSA cryptography in the 1970s.
If I had lived in the year 1900, I could have never imagined number theory having such immensely important applications, but in 2020, I sure as hell believe AlphaGo and these game solvers have relevance because it's already bearing fruit.
AlphaGo, for one, inspired many application papers. My favorite example though is of a neural net trained to solve CSPs through sudoko which was applied to the inverse protein folding problem! https://ostrokach.gitlab.io/project/proteinsolver/