I don't disagree that Chess, and Go, and very hard. I don't believe without a major mathematical breakthrough we will see either solved, ever. There just isn't enough possible computing power in the universe.

HOWEVER, arguing that they aren't solvable purely from a point of view of "the number of possible games / states is greater than the number of particles in the universe" type arguments is that there are many problems we routinely solve with massive search spaces.