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The play in the video is not normal because it's just too much
I think it is normal. There has to be some play in the splines with the lock ring off. Otherwise it would be a press fit and you’d have difficulty getting the rotor on and off.
I think the next step for @wenzovic is to try another rotor or take try the lock ring with two shims, take the shim from the rear lock ring.
Edit - which brand of lock ring are you using?
I had a similar issue last year, SRAM (ofc) Paceline rotors on 240EXP hubs. Zyro said "send it where you purchased it from [you such and such]" so I bought another pair from where I got those from, Centerline XR this time. It worked.
The play in the video is not normal because it's just too much. The lockring can apparently hold up up to a point. Trying with XTR rotors it's minimal.