Its a bi-stable mechanism. Once you pass a tipping point, the mechanism releases itself.
Because there is a hard stop for the first part of the linkage on the rotating wheel, it can pull down the catapult. Eventually this hard stop no longer prevents the linkage from moving upwards, and the surgical tubing pulls it.
http://youtu.be/Gm96S8gdhR0?t=3m8s
If you look at this video, the screw catches the first part of the linkage, allowing the catapult to be wound back. They cut away just before launching, if you continue rotating the gear further, the direction of the force on the linkage switches from against the screw to free allowing the linkage to snap and release.