Or can it run PSPs game as they were originally released?
They need to be ported. The official line is that the PSP Xperia is a "Playstation Phone" and not a "Playstation Portable". Seems like a bit of a letdown if you ask me. Here is a quote:
"[Xperia Play owners] will have to repurchase the games, so it's not totally integrated. I think the exciting thing is that there are games which people are very, very aware of."