I'm not sure that the genre is entirely new. There are a couple lines of predecessors.
First, games like Ghosts n' Goblins, that feature three main components: insane difficulty (including constant death), infinite continues, and reasonably frequent checkpoints. The ideas with these games is that the player is required to execute a short series of challenges near-perfectly in order to progress, but that the player will have unlimited chances to do so, and will not be punished (much) for failure.
Actually, the Ghosts n' Goblins/Ghouls n' Ghosts series is about the only example that I can think of that really fits that description. The Mega Man games are close, but don't actually offer infinite lives (Wily stages must be done with a limited number of lives, or the player is sent back to the beginning); Ninja Gaiden is difficult enough, but places its checkpoints too far apart (i.e. punishes death too severely). There are probably good examples out there, but none spring to mind.
The big difference between GnG and IWBTG, though, is that GnG relies on haphazardly arranged hordes of simple-minded adversaries, whereas every aspect of IWBTG is placed with deliberation. As my brother (who introduced me to the game) put it, when contrasting the IWBTG with Ninja Gaiden:
"IWBTG is pretty meticulously planned out, and is intentionally an asshole.
You know that in any situation that seems impossible, isn't.
"Ninja Gaiden programmers just threw a bunch of random shit together, made an
enemy spawn every time the screen moved 4 pixels, and called it a day. More
often than not there really wasn't anything you could have done to stop
those 20 birds from raping you while you were in the air (Except happen to
have the power up that puts a ring of fire around you that is completely
useless in every other instance).
"The best part about IWBTG is that once you get past something, it seems a
million times easier if you have to go back and do it again. Things seem to
go from 'how the fuck am I supposed to do that?' to being minor annoyances
pretty quickly."
The other sort of games that come to mind are the early adventure games that required constant trial and error, and punished nearly every error with death. Leisure Suit Larry, Space Quest (the original, now), Hitchhiker's Guide, Zork (to an extent). These were games of severe frustration and constant threat of senseless death. The big differences here, of course, are many: the games require no manual dexterity, the player could save at any time, and the player could unknowingly enter into (and save his/her game in) impossible scenarios (e.g. by destroying a necessary item, leaving an area too soon, or setting a deadly force into motion).
I don't think that "survival" fits IWBTG very well. The survival genre is not so named due to constant death, but rather due to the plot, which generally involves a person stuck in a deadly situation and attempted to escape. This sort of plot is in constrast to adventure, fighting, stealth, shmups, or other games that involve characters deliberately confronting deadly challenges in order to gain some reward or defeat some latent evil. Survival games also tend to emphasize health/resource conservation in the long term, such the player is not simply moving from one safe spot to another, but must make a thoughtful, game-long plan for continued survival.
IWBTG requires the player to survive, of course, but no more so than Super Mario Brothers or Double Dragon. Nearly every game is a survival game by that standard. The comedy designation is probably fair, however.
I don't know. It's probably not adventure, because you don't get power-ups and don't really unlock new areas (save for the last one). It's a platformer, but that designation kind of misses the point. To me, the game is primarily a puzzle, with each room presenting a seemingly impossible challenge that is met by discerning the limits of the Kid's abilities, and the full danger of the environment. Perhaps the proper genre designation is "Morbid Puzzle Platforming Frustrator."