Hi, Welcome to the Silverwing 600 Forum. We ask that you be polite and also introduce yourself on your 1st post. The members are friendly and helpful so just have fun. There is www.maxi-scoots.com site that is geared for all scooters and motorcycles.
Your Chain appears normal as well as your sprockets. Some slack in the chain is required so that nothing binds, New chains have some slack and appear like yours.
I would only suggest more frequent oil Changes. Happy motoring lloyd 193.
Thank you! I hoped this answer. Yes, I plan more frequent oil change, and in general much more care, than the previous owner... I have this SW since middle of Juny, thence I done and have to do yet some greater or lesser annoying repair and maintenance, what wouldn't do after a careful owner and a careful service station: all brakes, many body plastics and screws, all liquids, all filters, crankshaft left oil seal, crankcase right side sealing, rear tyre, lost driven shaft nut, ect. And a frame welding, what I will show in another topic, because it caused by steel material fatigue, so it'd be important to examine for others, too.