There is no earthly way that an app-store style platform for Windows would be backward compatible, but it doesn't have to be. New apps would run in a sandbox and only those would be allowed to use the slick new distribution system, go in the app store, etc. Legacy apps would run the same way they do now. Some day, there would be no more legacy apps but until then, the two types can happily coexist.
What they need is something like ".NET App Framework" that offers a complete platform in a sandbox. They could easily leverage existing Windows and .NET functionality to the point where the platform would be considerably more powerful than iOS/Android/WWW and very difficult to clone. Making it touch-friendly would be a good idea too.
This is a far better option for them than trying to clone Google's clunky web apps or start yet-another-smartphone-platform. There are really only a few critical things that allowed those models to successfully compete with the desktop, so figure out what those things are and fix them. Contrary to Microsoft gospel, the market is clearly willing to throw everything away and start from scratch, just to fix the bloody mess they made, so do it.