> Are browsers on mobile devices so sub-standard they don't fully support
> what we loosely call HTML5?
You missed something big here. In FirefoxOS all applications, and in fact the UI for every aspect of the device, are all implemented using Web standards --- HTML5, JS, CSS, etc --- and on a fairly low-end device too. See https://github.com/mozilla-b2g/gaia
If anything, FirefoxOS is proof that HTML5 *is* a viable platform on low-end devices --- at least, if you run it closer to the metal than is done on Android or iOS (where Web apps are forced to run above, or at least alongside, large "native" frameworks).
FirefoxOS has an app store, because stores turn out to be useful for discovery, management and monetization. But that's mostly orthogonal to the platform and APIs.