Diablo, the series is a dungeon runner.
Unless Diablo 3 changed its core design philosophy, I would say the entire series qualify to the point that they're pretty much the standard for what dungeon runners are supposed to be.
Furthermore, action RPG is not a genre that excludes a game from being a dungeon runner.
Dungeon running is a concept that describes the nature of adventuring and the setting within a game, not the combat mechanics.
In Diablo, especially the first, and the second, the entire point of the game is essentially dungeon running.
You gear up, and run around in dungeons, avoiding traps, killing mobs and gathering items. That's basically it.