Exactly how do you quit this program? I searched all over and the best I could find was "Crtl+Y" which does not work.

This is not a problem if you are running virtual DOS, since you can alt+tab to Windows. If you're running DOS there does not appear to be a way out.

Any ideas?

Ctrl+Y is correct and working here. Did you keep in mind that your keymap might differ from US layout? I have to press Ctrl+Z for example, because the Z and Y keys are swapped. Also, quitting the game isn't immediately noticable. The game's last screen stays, and even when you type something, it's in a larger than normal font, because the screenmode isn't reset to DOS default.

Most of the PC games as old as Alley Cat weren't meant to be "exited" anyways. In that time, hard drives were not invented/almost nonexistant and you needed to boot with a bootdisk. It was easier and faster to simply hit the on/off or reset button back then.