Harold, I don't think the play is from the gearshaft, I think it's from the sprocket. I just did a rebuild and when I put the aftermarket sprocket back on, it had about 3 times the play that your video showed! It was a pretty new srocket, but then I took a Puch original off another E-50 and it was nice and tight - no play at all. I think these aftermarket sprockets are made from shitty steel - you hold it next to the Puch original and you can just feel the difference in quality.
In your video it doesn't look like the shaft is moving at all, just the sprocket going back and forth.