Axle movement?

Yes use a little extra care when installing vintage aluminum mag wheels.
They make many different kinds of lugs and washers for different brands and styles.
Wheels, lugs and washers all have to be matched to your application. If you are unsure
Don't guess. Use thick large diameter washers if at all possible. They distort less when tightened more than normal.
Also I have never had good luck using a torque wrench on the old aluminum wheels
It is more of a feel thing. Even tension on all 5 increased gradually in a criss cross pattern
Tighter than normal torque specs works best. Tighten them like you don't want them to come off. Take for a short stop and go drive and re snug. Good to go. Some folks check them often but if put on right I never do anymore. Even the unilugs work fine with care.
Not good when they come off. I had one loosen up on me once 35 years ago.
I felt something was wrong and stopped to find my left rear wheel had wobbled as you speak of.
Was only being held on by 3 nuts and they had backed off a lot.
I have been careful ever since and no more problems with them.
Didn't mean to go on and on here but after watching your video
I think the wobble you felt had to be the wheel being loose.
I would check them all if I found 1 loose. Scary. Be safe and have fun.