> The thing is, Firefox for desktop and Firefox for Android could implement those APIs and then implement 'installing' apps from the web that use those APIs, making them cross-platform. And, since the APIs and all code is open source, other browser makers would be free to implement it.

This is already the case - check out http://marketplace.firefox.com/ on desktop or android Firefox.

However - note that app developers can choose to only support certain form factors. Many do support desktop however, for example https://marketplace.firefox.com/app/pasjanssolitaire

Desktop does not support all of the new WebAPIs currently though (https://developer.mozilla.org/en-US/docs/WebAPI), and certainly some may not be relevant on all platforms.