The fact that they release The Gift of Music as the first single also hints towards the idea that the first two songs a) won't be actual songs or b) will be instrumental, just because it wouldn't make sense to release a song from a rock opera that's set somewhere in the middle of the story. At least that's how I see it, I don't know how they handled that with SFAM.
Like a few people already said, I think Descent of the NOMACS will probably be some sort of introduction to the NOMACS (heavy, weird opening to the album) while Dystopian Overture will be serve the function Overture 1928 had on SFAM (thus, being instrumental).
I feel like the songs marked with the NOMACS will be tied together (using the same riffs or variations thereof) and am fairly certain that they will be some sort of music, but not the pretty kind. Maybe something heavily distorted, maybe even noise or industrial-ish? It's also notable that the marked songs all sound like they would be NOMACS songs, even if there were no little NOMACS next to them (Descent of the NOMACS, The Hovering Sojourn, Digital Discord, Machine Chatter and Power Down all relate to the machines in some way)
Judging from the track list, I would guess that at least these songs are actual, longer songs:
The Gift of Music
A Savior in the Square
Heaven's Cove
Whispers on the Wind
Hymn of a Thousand Voices
Thats just 5 songs, but thats because I'm only listing the ones where I feel certain that they could be indeed actual, standalone songs. There probably are a few more. Judging from the structure of the last few tracks, I'm also feeling that Astonishing (even though it's the title track) won't be an overly long epic, but more of an epilogue. If I had to bet money on it, I would guess that Hymn of a Thousand Voices is the climax of the story. Our New World could be a short spoken intermission, Power Down will probably be the ending of the NOMACS (being the final part of the 5 part NOMACS "song") - the story would be pretty much over by this point. I can't see how Astonishing would make sense as a final kick-ass epic song here. It could be a lot like the latest Muse album where Drones (also the title track) feels a lot like it's the last part of the song before (The Globalist) and basically serves as a moody way to end the story.
That's just my thoughts. Oh, and I don't like the album cover that much.