Don't print the "assembled_arm_preview" file. That's just to help visualize where all the parts go.
Print one of each other file except for two of "toothed_grabber_arm".
Pin everything together using straight pins as shown in the assembled photograph. Two of the end caps that print with the top section are for the moving section. Little pieces of rubber bands can be pinned on the bottom to hold the arms open or closed. Superglue all the pins in place.
Enjoy your newfound ability to grab things!