I have nothing to do with this service but I find it definitely compelling. Indie Game Stand only features one new game every four days (so even if you're accepted you likely have to wait to launch.) As for Desura, that looks like another good option, but is still quite a bit more involved.
If I made a game (a 48 Lundum Dare game like in the example page, for instance) and just wanted a way to put it out there immediately with little effort and no need to join a community or anything, itchio provides that option. That's what is compelling.
As the others pointed out, most of us don't want yet another game distribution service -- we already have a few.
[ As an aside, FTL is apparently on sale for $5 for the next couple days. I recommend this game to anyone and everyone who ever enjoyed an episode of Star Trek or Firefly.
Day[9] Plays FTL: http://blip.tv/day9tv/day-9-s-day-off-p1-ftl-faster-than-lig... (how I discovered the game)
/aside ]
Steam, even with Greenlight, is intended to host a curated selection of games. That is part of (or at least it traditionally was) Steam's value to consumers, but it has the side-effect of introducing bias against small, rapidly-developed, prototypical or otherwise less-polished games.
Here's a niche: Some people make neat game prototypes for competitions like Ludum Dare with a surprising amount of potential. Not everyone can afford to quit their job to turn their prototype into a well-polished product that can succeed on a popular app store or be crowdfunded (nor is every idea mainstream or even good enough to warrant that), but they are probably capable of at least cleaning up their prototype a bit and adding a decent set of levels or other content.
If someone makes a generic but fun game for Ludum Dare (say, a pixelated-platformer with a gimmick), I'd probably be willing to toss them a few bucks, mostly out of good will, for a more-polished but still quickly and cheaply developed successor. Whether they use that money towards developing an iteration that can succeed on a popular crowdfunding site (which are being quickly taken over by marketing experts) or as pocket change is fine with me.
This use case could be even more well supported by a Bandcamp-like donation system (which is what "pay what you like, or nothing at all if you are aware that you are allowed to enter $0" effectively is).
I'll end my reply by wondering aloud if a new generation of freeware games would ever be viable -- high-quality niche games released for free (and possibly open-sourced), and supported by a no-strings-attached donation scheme.
There are many other services already though that provide similar functionality, such as indie game stand, desura, etc. that have none of the restrictions you've mentioned as being a reason to not use Steam.
So again, what makes this service compelling?