By the looks of your video, the gear lever return spring, part number 20 is functioning properly however, my thoughts are that part number 18 is faulty.
It's this that moves the selector drum through the gears, it's held in position by part numbers 19, 23 & 26, its somehow been dislodged from its correct position on the gear shaft which is causing your issues.
Sometimes this is caused by a fall of some kind.
If it was just worn you'd be able to change gear randomly and it's my feeling that part number 18 has lost its position on the gear shaft.