The amount of play in your video would not concern me, though its a bit large, the chainwheel can only wobble when the clutch is pulled in anyway, and the range of movement possible (by the plates having a small gap when pulled in) is probably lesss than in your video, the centre of the clutch bearing is clamped by the clutch nut so cannot spin so it can have a bit of clearance over the shaft I guess, albeit this could cause the chainwheel to be not concentric with the gearbox shaft so is not desirable!
The clutch bearing would have to be pretty tight to prevent wobble at tbe edge of the chainwheel after all....and even if like that when new I suspect a bit of wear would allow the wheel to wobble.
I have seen it said that the position of the outer race in the chainwheel is crucial to prevent clutch drag and maybe wobble, if the position is wrong it certainly can cause drag, and certainly if the position is adjusted so the chainwheel is pushed close to the backing pressure plate (behind the chainwheel) wobble can "appear" to be reduced anyway, but I have to say I am not 100% convinced the position is supposed to be used to adjust this ......but it might be worth checking it is correct, though I do not think the correct position is any manual I've seen........