I'd bet you could do it almost exactly like they showed it, no expensive LCD needed. Either an X/Y pen (like those pens that remember what you write), or just a very simple piezoelectric touchgrid with no attached display. The microprocessor and electronics would have to be highly integrated and very specialized, but you wouldn't need much CPU power if you simplified it to the bare minimums to get the job done.

The only thing the microprocessor would need to do is remember a series of impulses from the piezoelectric grid, in order, and then play them back, in order. A small and simple math calculation to determine the amount of wheel turn to reach the next X/Y point, some tweaking of values to fit the real world, and you're done.