You can imagine that playing streaming video on a computer having a weak CPU, which also serves as a GPU, can create some head-scratch. And of course it did to me.
Here is what I could collect by doing some research on search engines and fora.
Add some support to the HD2500 (the GPU inside the G1610):
That's the hard part.
However, with this working, youtube still wont play video on neither Safari nor Firefox, which both make use of Adobe's Flashplayer.
And here is the solution to the problem: Google's Chrome Browser. Chrome has got builtin support for streaming video. And indeed, with Chrome, the Wimp (G1610 Hackintosh) is able to play youtube content.
And yes, also in full-screen, but forget about full-screen again... not enough compute power in this computer!