Does Slay the Spire look like the sort of thing Hearthstone’s dungeon run is trying to do? Both are basically what the title says. Monster Slayers is another that came out last year, which I had not noticed. Guild of Dungeoneering does something similar, although there is limited deckbuilding scope within each dungeon run, and the dungeon opponents are less randomized than is common in roguelikes. (Hand of Fate from that post uses constructed decks, rather than deckbuilding within the dungeon, with a lot of roguelike randomness.)
This could be a new sub-genre.