The main issue at the middle level is that people don't push to the next level of thinking, despite often thinking that they do. The reality is that most people have the thoughts but not consistently. Or, they have the thought, but don't apply it (well) to their decision making.
(I'm going to butcher this concept for this example)
Level one - You play your cards. You look at what you've got; you do stuff that has a big effect based on what you have in your hand. Your opponent's counter-play options aren't considered.
Level two - You now consider that your opponent might counter the cards you play in some fashion, and you adjust accordingly. This is the level most people are at. ('If I play BIG CARD and he just kills it with EASY COUNTER that would be bad...let's hold off on it until there's a lower chance of that happening...')
Level three - You now consider that your opponent is making the same kind of decisions you are. The game becomes more about information. You know that when X card is played, it indicates certain other possibilities. And, you are aware that your opponent might be making the same considerations about you, so you consider the plays you make in the context of how they might be perceived. (A lot of this becomes near-autopilot because of the sheer volume of games put in - often thousands -> tens of thousands).
This is the short version of the concept, but it applies to all games that have incomplete information, MOBAs, Card Games, RTS, and so forth.