Not seeking to troll you at all, but this is at a lower level than your window manager. This isn't talking about "desktop" in terms of KDE, GNOME, etc, this is saying that Mir (which is a replacement for X) will not support running non-Unity X clients as wholeheartedly as it will Mir clients.
This means that it's unlikely that awesome will run as well on Mir (being an X client) than it does on X itself. The Mir developers will ensure that Unity runs well as a Mir application. They will not be investing time in ensuring that KDE, GNOME, or awesome run just as well.
While the term "desktop" is being used here, it's somewhat misleading. These are all X clients (applications). They make use of the display server (X). Ubuntu is getting rid of X as a display server and is moving to Mir, a completely different kind of display server. While they plan to include some ability to run X applications under Mir, that effort extends only to Unity software, not anything else. If your non-Unity X application runs, then you're lucky. It's not because Canonical is watching out for you.