I've done a bit of digging and found out that this is in fact a Kontax KS80 Solar engine, and is designed to work in a sunny window no problem, but will in fact work from any sufficient heat source, as demonstrated here.
This is a demo of a Stirling Cycle Engine desktop model that I bought recently second hand from an old odds and ends shop, and as can be seen it works perfectly, running off only the heat coming from my monitor.
What's happening here is quite straightforward.
The big foam cylinder is called the displacer piston, and what this does is basically ensure that most of the air inside the engine is either towards the top, or towards the bottom of the main chamber. It isn't a tight fit; air can get around it no problem, so when it's at the bottom most of the air is at the top and vice versa.
The cylinder actually responsible for generating the power is the little grey one at the back; that's a sealed piston called the power piston which is actually made of graphite to provide a good seal while also being low friction.
The process is as follows. When the displacer piston is towards the top of the chamber, the air is allowed to come into contact with the lower face of the chamber, which is warm from the heat coming off the monitor.
This causes the air inside the chamber to expand slightly. The air has nowhere to go, so the only way it can expand is by pushing the power piston up. Everything is connected together via the linkages to the big flywheel at the top, so the act of pushing up the power piston then makes the displacer piston go down to the bottom.
That then exposes the air to the cooler top plate, causing it to contract, pulling the power piston back in. This then moves the displacer to the top and the air to the bottom, where it can be warmed again and the whole process starts over.