First, a quick recap: Having first praised the parts of Diablo III that worked, we then went on to discuss D3's genre, and established that it's definitely an RPG, and not an action game.
It's not very effective as an RPG, though, having neutered or entirely removed most or all of Diablo II's genre-defining RPG systems, while failing to replace them with robust collision-detection-based action mechanics. But there are plenty of RPGs that don't have especially strong RPG mechanics, or any action mechanics to speak of. Many of them have still come to be very highly-regarded as examples of the genre, in spite of those shortcomings.
How? Simple: by telling a compelling story.
Sure, ARPGs are generally not story-heavy, and their largely linear plots don't normally lend themselves to replayability for the story alone, but a good story can carry you a good long way into a game, compensating for shortcomings in other areas until you become so immersed in the game that the flaws cease to matter. And the Diablo series has a history of solid lore and story elements. The original Diablo game was chock-full of lore, otherwise known as environmental story-telling; Diablo II's story is generally regarded as one of the best ever for the genre.
This should have been an easy win for Diablo III. Instead, it became one of the game's most-hated elements. Players hated the story so much that Blizzard added an entire play mode that allows them to avoid engaging with the story entirely. And it's weird, because the basic beats of the story, as they appear in the game's gorgeous cinematics, are basically fine. Seriously, they are.