They're not the only company out there doing it - Steam has it's share of old games, as do gametap and the other download services. But they are unique in several ways.
Firstly, you're not just buying the game. These are games from the era where the box art was beautiful (because sometimes the game wasn't) and the manuals were detailed (because there was no GameFAQs to tell people how to play.) So GOG give you the manual as a PDF, to take home and print (this is key for games like Beneath a Steel Sky, which used the manual as DRM, and for Fallout, which uses the manual as a 2-semester module and doorstop.) They have a virtual shelf, where you can arrange all of your games and see the box art. On top of that, they give you much more - icon packs, desktop wallpapers, soundtracks - whatever quality bonuses they can scrounge up for a game, you will get access to - even if you already bought the game when they acquired the bonuses.
Secondly, you're buying *THE GAME*. This is key to why I'll buy my games from GOG over Steam for preference.
When you buy a game on Steam, you're buying the ability to download the game through Steam, launch and play the game through Steam, but all at the discretion of Valve. If the servers go down for good, you can never download the game again. You can kind of back it up, but it's a bit technical and not something that most people are likely to do.
When you buy from GOG, you download an installer specifically for the game you bought. It has no checks in it, no DRM. In fact, the worst DRM you'll run into is in-game manual lookups, which is another reason it's key that they provide the manual. Install, run. If I want to back up my game, I just pop the installer onto a CD. Need to redownload it? There are no limits on how many times you can get it from your account (pay attention, Codemasters.)
All of this makes GOG a very compelling service for me, which makes it really hard not to buy incredibly good games like Sanitarium, *even when I already own them*!
Maybe they'll have the soundtrack...?