Yes.
I think the picture on that page is wrong, as it says that it is a USB Penta Switch, but the connector in the photo is the 9-pin Atari style connector. Regardless, there is also a
9-pin Penta Switch, which is generally used for wheelchair control.
Of those nine pins, five represent the five buttons of the penta switch, and when each button is pressed, that pin is connected to ground. They are just switch closures.
So yes, there should be an adapter (often called a "squid") that splits that plug out to five 1/8" jacks, for switches. I *think* that they exist. I would go dig around in our power wheelchair lab, but it is in use at the moment. I will try to look later. If it doesn't exist, it can certainly be made by someone with some soldering skills.
I don't know if that would be the easiest solution, and you might be better off going with a different controller, or using something like Joy2Key to see if you can re-bind the buttons, but what you asked should be possible.