Actually the answer above did not fix the problem.
The problem was that eventhough the error dialog box was saying that the game did not detect a DirectX 9.0c compatible video card, the real problem was that it was directx 9.0c SOUND drivers that were required.
I upgraded my motherboard sound drivers and it all worked fine.
By the way, the problem was actually being caused by The Sims 2 expansion kit: the Teen Stuff and the Kitchen & Bath Kit which both required Directx 9.0c sound. When I removed these 2 kits, the The SIms 2 Appartment Life would work fine as well (before I even updated my drivers).
Case closed!
Thanks for the answeer anyway!