Loose rings will sometimes make that noise.
What that video is illustrating is a leaking head gasket, and yeah, a leaking head gasket can sound like mechanical looseness of parts. you might have a warped head
I recall an old Cycle World article that was discussing rod bearing sounds, Because 2 strokes have no reversal of forces on their rod bearings, ( it's the reason why most 2 strokes use needles and rollers top and bottom ends.) you will not 'generally' hear a 2 stroke make rod noises before it's too late. I've had direct experience with a needle bearinged 4 stroke Ryobi 845r weedeater engine that was destroying it's upper needle bearings. It's was making quite a clicking racket while it ran, especially at idle when it's under a lot of manifold vacuum.
You might want to disassemble the pinion/clutch ring gears and see if there some bad free play in the keyed shaft off the crank.