My understanding is that we have achieved very good pattern recognition, but that's only one aspect of cognition. IIUC a large part of our brain works that way, but for example there is also the language center which has recursion.

Also I don't think logic is just word games (could be wrong).

I'm sure we'll get there but I don't think this is it. E.g. AlphaGo was really good because it combined machine learning with tree search algorithms. Seems like logic and language and world knowledge could be combined with the excellent pattern recognition we currently have, merging first generation AI with the current stuff.

I have no idea how! I'm not in this field, just watch from a distance.