I'm not so sure about it being a rotary joy. It appears to be an optical-analog; ie, it's using optical encoder wheels instead of potentiometers to measure how far the handle has traveled. But there is that odd 2nd circuit board above the one with the encoder wheel, can't see what that thing's doing, I suppose it could be for a rotary function.
The only game I can think of offhand to use an optical-analog joy is Aztarac. But that one should have a triggerstick handle of the Gorf/Tron variety, not that funky firetop thing. And the base doesn't really match the diagram on page 22 of the
Aztarac Manual, so I don't think it's just a case of a wrong handle on an Aztarac stick.
