Except that Diablo (any of them) lacks the one major genre-defining game mechanic of a Rogue-Like and that's "you have a single life and if you die, you have to start over."
Yes, there's "hardcore" mode in Diablo II (and presumably Diablo III, but I don't know for sure) where you get one life, but that's a specific setting, not the game's default. In a Rogue-Like, it's expected that you'll die a lot and have to restart the game many times. In a well-designed Rogue-Like you'll still gain something — experience, skills, items, etc. — from each run, so your time isn't wasted, but the one basic game mechanic that all Rogue-Likes share is the "single life" concept.
The top-down view of a dungeon has absolutely nothing to do with being a Rogue-Like. There are card battlers (examples include Monster Train or Slay the Spire) or Action-Platformers (like Rogue Legacy) or even Puzzle games (such as Ironcast) that are all Rogue-Likes, yet share little-to-no gameplay with Diablo and certainly don't use a top-down view.
To further drive home this point, let's go for a different comparison: Action games vs Flight Simulators.
No one in their right mind would ever classify Dogfight 1942 or the Ace Combat series as a Flight Simulator. Both Dogfight 1942 and Ace Combat are Action games that have no realism to speak of (you don't have to know a thing about flight dynamics or all the controls in your fighter) and was designed for people to "jump in, shoot stuff down, and jump out."
Contrast that with a real Flight Simulator, such as Digital Combat Simulator or Microsoft Flight Simulator, or even Dynamix's games (A-10 Tank KIller, Red Baron, Aces of The Pacific, Aces Over Europe) which are somewhere in the middle between serious Flight Sim and Action game.
All of those games I mentioned share certain qualities, such as you fly different planes or jets and shoot down enemy craft or potentially bomb land targets. However, the way they go about doing this is drastically different and the amount of knowledge needed to fly or even turn on your aircraft (seriously, there's a good 20-step process to even get the A-10 ready to take off in DCS, let alone actually flying it!) is so different between these games that despite looking similar, they share very little in-common when it comes to gameplay.
If we went with your definition of genres, Tawmis, we'd lump DCS or MSF in the same category as Dogfight 1942 or the Ace Combat series, and that would inevitably anger and/or disappoint players who were either looking for a quick action-oriented dogfight or a complex and serious Flight Sim.
This is why proper classification of game genres (preferably based on game mechanics and not look or feel) is important.
OTOH, I thought that sometimes DD "cheats" by stacking the odds against the player.
What's the point of playing a game if you can only do one thing and then have to wait 24 hours in real time before you can go again?
