Could be XP SP3 , maybe?
Nah, don't think that would be a reason, I have XP SP 3 on all my PCs and never had any problems with it (neither Dyson nor other games) - can't speak for the original poster of course. If I should guess I would say it's using OpenGL emulation instead of the graphics card. Updating drivers to a version with OpenGL support could help (at least I've heared of some ATI having problems with OpenGL, dunno, I don't have any).
Now, ontopic, I've also installed it on my old PC but only tried the first levels (the new version is much harder than the older ones, takes me quite a bit longer to beat a level now
Win XP SP 3
CPU: AMD Athlon XP 1800+ (1.51 GHz)
RAM: 512 MB
GFX: NVidia GeForce 4 MX 4000
Had several fights with about 100 units on a planet each side, no slowdowns.