I think that the way good games teach things is basically being engaging by constantly presenting content that's in the learner's zone of proximal development, offering any guidance needed for mastering that, and then gradually increasing the level of difficulty so as to constantly keep things in the ZPD. The player is kept constantly challenged and working at the edge of their ability, but because the challenge never becomes too high, the challenge also remains motivating all the time, with the end result being continual improvement.

For example, in a game where your character may eventually have access to 50 different powers, throwing them at the player all at once would be overwhelming when the player's still learning to master the basic controls. So instead the first level just involves mastering the basic controls and you have just a single power that you need to use in order to beat the level, then when you've indicated that you've learned that (by beating the level), you get access to more powers, and so on. When they reach the final level, they're also likely to be confident about their abilities even when it becomes difficult, because they know that they've tackled these kinds of problems plenty of times before and have always eventually been successful in the past, even if it required several tries.

The "math education is all about teaching people how to stay focused on hard abstract problems" philosophy sounds to me like the equivalent of throwing people at a level where they had to combine all 50 powers in order to survive, right from the very beginning. If you intend on becoming a research mathematician who has to tackle previously unencountered problems that nobody has any clue of how to solve, it may be a good way of preparing you for it. But forcing a student to confront needlessly difficult problems, when you could instead offer a smoothly increasing difficulty, doesn't seem like a very good way to learn in general.

When our university began taking the principles of something like cognitive apprenticeship - which basically does exactly the thing that Viliam Bur mentioned, presenting problems in a smoothly increasing difficulty as well as offering extensive coaching and assistance - and applying it to math (more papers), the end result was high student satisfaction even while the workload was significantly increased and the problems were made more challenging.