Telengard
Arcane
These sorts of divisions are discussed by designers all the time. Because games are designed to appeal to people. In order to appeal to people, data is collected, grouped, and and made presentable for the higher-ups.The danger of simplifications like this is that you believe they truly portray reality, and thus everything you elaborate from here is invalidated. There have never been 4, or 7 types of RPG fans; most RPG fans are appealed towards several of the game aspects, and often about all of them, with different priorities, or at the most not caring about some of them. And these preferences evolve within time, or change for just a particular game which is unusually good in one of its aspects. Otherwise, we'd have 3 or 4 separate genres.
The seven types were released in a popular book of the time, and while I did not agree with dumping tacticians and grognards into the same category, it's not like they were enough left in RPGs by that point to make any difference.
The whole idea behind the power fantasy is that your character gains power, and lots of it, while the world remains static. You get to do to the world all the things you wished to do but couldn't. It is wish fulfillment, at its core. Everything in the world of a power fantasy is not a wall, but a speed-bump that barely slows you down. That is what feeds the fantasy, what makes you feel powerful. If you hit walls, you wouldn't feel powerful, you would feel frustrated, and the fantasy breaks.Power Fantasy can't exist without a challenge that you eventually overcome, and new challenges that keep your gained power being tested. At least for me and for anyone else not being an instant-gratification-whore.
However, with power gamers, when they speak of challenge, they usually speak of challenge on the character sheet anyways, not in the game. They want their mad character building skillz tested, nothing else. And that sort of "challenge" doesn't break the fantasy in the slightest, of course.
Who was it that liked the idea of incorporating large parts Unearthed Arcana into 2e, with its high-power spells and cartoon classes? And who demanded that rangers be super dual-wielders to make them like Drizzt? Who was it who even now calls anyone who asks for something different, like an Old West RPG, a retard? Why, it is the people on this very forum!This trend is not the fault of the RPG players, at all. It's the fault of the excessive mercantilization of the entertainment industry, and how the huge investments lead to "safe formats" that you can prove that returned the investments in the past.
And I'm shocked - shocked - that this is this case.