But other people are focused on trying to win a different game. So when they try to talk to each other about who is winning, they completely talk past each other. But when you realize that someone thinks he is playing a different game and you figure out what it is, you can have a much more productive conversation/relationship.

This is an important insight. I'll add that sometimes being able to understand the different way people think can simply allow us to realise that it is more productive to have no (or minimal) relationship without judging them to be poor thinkers. Judging them not to be 'thinkers' in your original sense at all can be a lesser judgement than concluding that they suck at it.