I agree. DD is like a real time RPG. ARPG's are more like adrenaline rushes, massive monsters, huge ass powers, like you are a mower and they are grass. They are fun, but they really are so lite on story, it's really misses out a chuck of RPG. And with the shear constant barrage and overpowering unlimited skills, tactics aren't much a part either. Just need to make sure your build can handle huge ass waves of mobs non-stop, that is pretty much the challenge.
DD doesn't play that that at all, it totally has it's own charm. Much more a RPG in a traditional sense in my mind. Almost like a genre that should have had many more entries in it, but never did.
I agree that DD is better than your description of general ARPGs, but I disagree that this makes it "not an ARPG". It's still a Diablo clone, it's just far better than Diablo because it has a deep RPG story and well written/designed quests. The ARPG/Diablo mechanics are still what they are though. That made it painful to play for those of us that don't enjoy that kind of click-fest. I tried and likely would have finished it if not for my teleport-losing tantrum, but it was a chore to clickity-click-click my way through it so I could try to enjoy that great RPG hidden behind the Diablo mechanics.
If only it were turn based... :-(