Hmm. That does seem like an effective form of classification - dual axis classifications, like the classic good/evil lawful/chaotic axes, are always very flexible, and almost anything can be divided relatively easily into the two sets of opposing characteristics like that.
The biggest problem, as has been discussed above, is the "Action RPG". You can easily see the issue just by looking at the wheel - action is on the opposite side from RPG. I see your point in that most of the time you can tell whether it's more action or more strategy by whether it is stat or skill based, but there's one problem with that - it only takes into account the conflict portion. What about the exploration portion? In all of these games, exploration, of the story and the world itself, is strategy based, not action based like a platformer.
In short, in the RPG you have the conflict, easily divided through mechanics into action or strategy, but you also have the exploration, which is almost always strategy.
Thus, the typical action RPG, like Bethesda's open worlds or Mass Effect, ends up evenly balanced again.