Diablo series is a hack and slash action game. Not really an RPG. All RPG's need to have these elements. Lets see how Diablo matches up.
1. Character advancement - You need to be able to get better and more powerful loot/ways to beat the enemies. Diablo passes this. You get more loot. And levelling is progression too.
2. Character emotional advancement - Your toon needs to be able to learn from the games experiences and react to things differently to things at the end of the game compared to the beginning of the game. - Diablo fails at this. Your toon reacts to things the same way in Act 1 as the later Acts.
3. NPC interaction - Lots of this in Diablo. So pass there.
So we get 2 out of 3. So it's not a traditional RPG. But an action RPG maybe. But there is so no emotional connection to the Diablo toons. They never tell us how they feel. They just listen and do as they are told. As far as I know the toons in D1 and D2 didn't speak at all.