Hm.
Writing Style is subjective, so I don't know how much of my feelings apply for other people. This doesn't read particularly well written to me, but I can't point to a specific instance, except maybe that the first sentence conveys no meaning (that isn't already inferrable from the title). I could suggest different phrasings, but I could really do that for the entire thing.
Content-wise, I'd ask myself "how can I describe the appeal of this story as well as possible in a few paragraphs?"
Speaking of which, what is the appeal of this story? We might have different ideas there.
I think it is that it's extremely intelligent, which sounds elitist but that's really what it is, and I wouldn't try to be coy about it. Real harry is severely outclassed compared to HPMOR-Harry. He'll take a chapter to accomplish what real harry doesn't get done in the entire novel. He'll concern himself with things real harry doesn't even grasp or understand. If you ever thought he did something stupid, here is someone who will correct it. In fact, if you were ever bothered by protagonists ignoring the third, smart option in fiction, this is a story which will be immensely satisfying. And even more, he will correct flaws you haven't even noticed before. And he'll teach you how rationality/the universe works in the process.
That doesn't really come through in your review, does it? You talk primarily about which people he hangs out with and then say that it's amazing. Which it is, but I only say that because I've read it. The only thing which gives you an idea of how extraordinary it is is that he befriends Draco. Other than that, it could be a fairly generic alternate universe fanfic.
I don't think this will convince anyone. I'd rewrite it with your version of the above in mind.
Not sure if this would have been useful, but here is not how I'd have witten the first paragraph (this would otherwise have covered your first two).
[[ blue birds bouncing before beige bandicoots ]]
I had completely forgotten that you are the one who showed me this story. I owe you so much! ♥