Bay 12 Games Forum

Permadeath: Sort of has it to an extent. Yes, it's possible to eventually accumulate shortcuts. However, there is always some amount of levels you will have to traverse that must be redone if you die.
Grid-based: Yes. Your movements aren't tile-based, but the whole game is built around a grid of blocks, each of which are the same size as you. Most of the platforming challenges in the game arise from finding a way around an impassable section of the tile grid (which, due to randomness, can totally happen). You can abuse the shape of the tile grid to take on creatures from a safe place in the same way you can cheese parts of DCSS and Angband.
Non-modal: Yes. Everything takes place in the same mode.
Complexity: Yes. The definition of Roguelike Complexity as described on that page is "the game has enough complexity to allow several solutions to common goals." This is completely true for every scenario in Spelunky, and the items you gain only increase potential solutions.
Resource management: Yes. Pretty obvious. In addition to "not die," the guns have bullets, your ropes and bombs have limited use, and you have to really ask yourself if you're going to lose more health trying to save that Indiana Jones babe than you're going to gain saving her
Hack-and-slash: Yes. Do I even need to elaborate? Most of the game is silly Castlevania hack-and-slash.
Exploration and discovery: Yes (mostly). I will admit that, once you know the level layouts, you can always head toward the general direction of the exit from the start. However, unless you're reealllyyy good at the game, exploration grants you gold, items and lots of other helpful things to make the next level less brutal.
Single player character: Yes.
Ascii Display: There's a mod for it, believe it or not
Dungeon: Yes. That's the whole game.
Numbers: Yes. The main point of the game other than getting to the end is racking up a high score. I can't remember but they MIGHT not show uses for limited-use items.