I still would try jumping the battery post term on the solenoid to the start terminal just to check and see before you pull it out and shim it. Such an easy thing to do.
At the point your video shows the starter should be spinning. Normally the bendix drives out much harder than that. Remember that its not allows going to hit the flywheel aligned every time. It could be a half tooth off and needs to have enough torque to drive in and mesh.
Give the jump test a try. A starter gear extending out is a pretty violent movement. Not like what yours is showing.