The old 68k Macs are emulated with Basilisk II, which shims the mouse driver so it can just take mouse events from the host OS and move the cursor to the corresponding pixel on screen. The PowerPC Macs and NeXT boxes are emulated with a lower-level emulator that wants to get raw deltas from the mouse, not an absolute pixel position. If you just wave the mouse over the emulator, you'll get something approximating the expected movement (but much slower); once you click on the emulator it captures the mouse and you can use it as intended.

I agree it would be nice to have an "untransformed" view of the screen; I suspect the site might have been designed with the expectation of a high-DPI screen.