Not sure if the top switch is supposed to travel with the downward motion as seen here.
nope. The top switch should be open then the relay is powered.
when checking switches, push down on the metal armature plate instead of the brown switch lifter ... at least as a fine check. If you push on the lifter, you will move the switch blades a little further than the metal plate can and the relay may not work correctly in real life.
if your vid, you can see the armature plate hit the coil top then the brown lifter keeps going until the top of the brown lifter notch hits the top of the armature plate. In actual use, it's the bottom of the armature plate pushing against the bottom of the lifter notch.
however, that switch stuck closed would just make the total in meter a bit unhappy ... if you even have one.
the first video implies the handle release relay is tripping when you are holding down the coin switch. Does it? The handle release should not trip until the coin switch goes back up.
if you push hold the coin switch down, you should not get 50VAC with the probes on the yellow (30) and orange/green (74-1) wires on the coin switch.
wrt adjusting switches on the line unit step-up relay, you can misadjust things to make a race condition that may work occasionally. A bad video on switch adjust is here. Coincidently, it's a coin/line unit step-up relay:
https://bingo.cdyn.com/slots/videos/Switch_Adjust.m4v