It does, but you need a power that would have been relatively powerful for the era. The computer I tested it on has an AMD Athlon 64 X2 CPU and an ATI Radeon HD 4670 GPU.
The demo is up to date, yes. If you are trying to use a touch screen, graphics tablet, or some other absolute pointing device, the cursor will not work in fullscreen mode (they will work if you restart it in windowed mode). Otherwise I have no clue what's going on.