Looks like they're using Web SQL for local storage. Mozilla foolishly (IMO) rejected this standard so they'd have to reimplement the storage layer with IndexedDB to get this working on FF.
WebSQLDB isn't really a "standard". The standard is "whatever version of sqlite safari happened to ship with" which is really not a tenable long-term solution.
Sure it is. Pick a version. Call it the spec and fork SQLite if necessary. You can't possibly argue that this would be more work than inventing a new, untested data storage model from scratch. This approach is exactly what ran the W3C aground in the first place.