korell: Have you tried installing the DirectX 9 redistributable package from the Microsoft Download website?
Win7 comes with DirectX 9.0L, DirectX 10 and DirectX 11. They are independent of each other. The thing is (and this is also true of Vista) DirectX 9.0L is not a complete DirectX 9.0 and is missing library files. As such, to get a complete DirectX 9.0 you need to download and install the redistributable from Microsoft. The latest is dated June 2010, prior to this it was November 2008.
Lastly, have you contacted GOG support?
For the record, I've 11 games from GOG installed and none have had any unresolvable game-breaking issues. I've also a fair few that I'm yet to get around to installing and playing. It is always a good idea to check the forums for known issues, I find. I had considered getting I76 but found that that game is extremely troublesome, mainly because its speed is directly related to CPU clock speed and therefore needs slowing down, so I haven't yet purchased it.
I hadn't heard about Win 7 having a subset, so I'll have to try it. I still haven't figured out how to actually contact GOG for support yet. I pick on the "contact us" link and all I get is technical issues, which just brings me here, and the rest are about payment or downloading problems with feedback at the bottom. If they mean for us to use feedback to contact over game issues it is REALLY a bad design on their part!
And lastly DO NOT BUY I76! I had the original back in the 90s, and had thought that like Redneck Rampage (the game that first got me shopping here) they had figured a way around the problems via emulation. But nope! The game is pretty much unplayable on modern hardware from what I've found. I've tried every trick and hack on the forums and between the graphical tearing and both my car and the AI partner simply unable to get enough speed to do the mission required jumps it is pretty much worthless.
But thanks for the heads up on DX9, I'll download and install it. You'd think though they'd give these games a few spins on various hardware before certifying them. I honestly can't see how they could say I76 is working, seeing is how I have tried two different OSes and three different hardware setups and it is still a mess.