I believe so, though I’ve heard the first few moves are now randomized, as only perfect play, rather than all board positions, is solved.
Of course, every perfect-information deterministic game is “a somewhat more complex tic-tac-toe variant” from the perspective of sufficient computing power.
More strongly, is there any reason to believe that people are more likely to “click” to rational beliefs than irrational ones?
As an example, papal infallibility once clicked for me (during childhood religious education), which I think most people here would agree is wrong, even conditioned on the existence of God.