Service Workers are also in Firefox Nightly right now, but are hidden behind an about:config flag until the feature is fully baked.

https://developer.mozilla.org/en-US/docs/Web/API/Service_Wor...

http://caniuse.com/serviceworkers

There's also the Application Cache, which has been fully supported in the stable versions for a while now.

https://developer.mozilla.org/en-US/docs/Web/HTML/Using_the_...

http://caniuse.com/offline-apps

And of course, FF for Android has an "Add to Homescreen" button too.