OK, for a minimalist style, I would say this comes close, but it's not quite there. It's cleaver, it's catchy, but there's still something wrong with it.
What's that? Unity. Especially near the beginning of the song, it goes through several shifts without any unifying element to tie it together (except for, in some instances, a common theme). There aren't even any transitions to speak of.
I also noticed some notes clashing in the section around 0:40 - just a quick observation.
And, as others have mentioned, it needs a little more to spice it up. I would try adding some harmony - my observation is that all the parts play pretty much the same notes, just at different octaves.
I'm really debating what to give this, as it's almost there. But, it could use just a little more work. So, my vote's "no".