The screenshots clearly show an iPad-friendly UI. Sounds like you got the old iPhone-only app - likely the app hasn't propagated to all of the App Store yet.
Same thing happened to me, I did however just read on another blog post that its apparently cached and propagating through Apples servers. So I guess try again in a few hours.
EDIT: I downloaded via iTunes and it worked, downloading via my iPad seemed to download the wrong version. So I guess its proportion, some servers probably haven't been updated yet.