The latter Gomog link should be useful to you I think.
I've looked at your first movie several times and can't make my mind up as to where the problem really lies. I have had a tyre that was out of round but I've long since replaced it with a good one.
If the rim is ok and the tyre isn't, a problem that come to mind from bicycle wheels, is the tyre mounted correctly? If yours is a tubed fitment you could investigate this by letting the air out, breaking the seal and reseating the tyre. Easy on a bike, not too bad on a vintage trike but will be a bit of work on a car tyre. A friendly tyre mechanic at tyre centre ought to be able to quickly do this.
If the tyre is tubeless though, unless the tyre is defective, I very much doubt the seating is incorrect as the fitting method normally precludes this.
