Topic says it all. Just found DK2 here, want to play it so badly, but I don't know if it works on Win7.
I got the original at home, but I'm too lazy to do all that stuff with compatibility and shit to get it running.

It works like a charm, I can assure you of that. For me, it even works perfectly in 1600x1200 with DirectX enabled. Should it ever act up, you can find lots and lots of helpful threads. The worst thing that can happen is that you'll have to switch to software mode. Other than that, I don't really expect any trouble.

So just buying the game here, downloading the installer and installing it enables me to instantly play it without problem?

Yes, chances are good. Of course, depending on your computer's config unforseen problems might arise, but should this happen, you'll find lots of helpful advice here. Oh, and by the way: you absolutely need to install the Hardware Acceleration Fix that's stickied here in the forum. It's what enables DirectX acceleration for DK2 at all. For me, it worked like a charm.

You can contact Support and if they can't get the game working, you can get a refund.

It works fine for me on Win 7 X64, all I did was turn off Aero (which I do anyway as I don't care for it) and its smooth sailing!