those are definitely directx problems. I had a video card that was overheating and had artifacts like that.
I would try two things:
1. Make sure your laptop is nice-n-cool so your video chip (GPU) isn't getting too hot, maybe even lower the graphical settings.
2. Install Component: d3dx9
which version of Wine are you running?
Did you install any other components or did you use the PlayOnLinux script?
I'm glad it installed and is kinda running, I need to test my Rollercoaster Tycoon 3 also