This is very true, I never thought of it. Maybe the difference is that we always knew that AIs would easily win in FPS games. Whereas Go, Chess or Shougi were considered as a proof of human intelligence, for a very long time. Discovering, after all these years, our history, that a machine can now beat us at these games may be the major difference.

Maybe for these games to keep popularity, we just need to update our perception of it. The same way we do with FPS games. Yes, we know a bot would do better - but that's not what matters.

Another thing, as said in other comments, is that we can learn from bots. New strategies, new patterns. AFAIK, this is not happening in FPS eSports scene.