The motor mounts to a stand-off/adapter (square block item) and the stand-off/adaptor mounts to the plate on the side of the machine.
The motor has a coupler on the shaft that also interlocks to it complementary part on the machine side.
I cannot see the details of how the machine-side coupler part drives the axis shaft/screw.
The stand-off looks like the NEMA type on THIS page.
I found THIS link on their site. Download the manual and several pages into it you will find a diagram showing the mounting of the motor and associated parts.
Good Luck! That looks like a great machine for a school program.
-=Doug