I think I've figured it out...
The 'Alternate Reality' / alternative version of the album is the real-life way Muse would have 'traditionally' recorded their material, ie big orchestras, gospel choirs, etc.
Tracks 1 to 11 is actually the simulation of those alternate tracks!
Muse may have given us one album, but we can experience it in two different dimensions: As a simulation or as "reality".