I'm a Smith Corona Master Mechanic, Can't see much from this video

Looks like the return gear pack is stripped, if the carriage will not move back by itself, by hand, then that needs to be troubleshooted to figure out why. If the carriage is stuck that is probably why the gear got stripped out, I have nothing else to go on. Lots of things can cause the carrier to jam, even if the ribbon is installed improperly can cause the escapement to jam. If you move the carriage by hand, using the carriage release levers, all the way to the left and butt it up against the left margin it will reset the return clutch. I have found it difficult to try to help people online, long distance, one must know the theory of operation just to start troubleshooting.