I think it best to check the whole electrical pickup system in the model. I noticed you had to turn the throttle way way up before anything started to happen. Your model should be moving by atleast 1/4 throttle, not 2/3’s to 3/4’s as I saw in video.
Clean the wheels.
Check wiring for connection. (at both ends) and both sides + and - . (Red and Black wires)
Check the wires themselves for brittleness, conductivity. (requires an ohm-meter). Even replace them with a larger gauge wire if needed.
Check the metal contacts touching the wheels, polish if necessary. Are they worn?
Ofcourse cleaning and lubing the mechanical works is always a given.
Check the motor itself - brushes (reshape or replace as needed) - communtator (make this part nice and shiny!). Remove any fur balls left from previous owner.
Check to see if not only your positive side is conducting, but also check your ground side. (ohm meter again)
An easy way to check your electrical thru-put is remove motor (and light) and replace with voltmeter leaving all wiring/pickups/contacts in place. Take a reading. It should match the track voltage. If lower, then you have a bad electrical system. If they match, the problem is in the motor or gearing.
While you have the motor out, free wheel the model on track. Does it move easily or hard to push? If easy, then you know its the motor. If hard, toss that puppy on the grease rack and lube her up. (you may have to remove an idler gear or two for this test)
While motor is out, you can hook it up to your transformer and test it all by its lonesome. Check for sparking, over heating, and quite possibly smoke.
Lastly, even though we saw your train move, are you sure your electrical from transformer to track is ok?
These techniques and those listed above by others are generally the care and maintenance of model trains.