Yeah, the three thin wires can just be left disconnected. The black will kill the spark/engine if its grounded to the frame/case etc.
The other two just go to the lights/horn. On some model/year variations one goes to the tail and the other to the head light, but other times the two power wires are just joined together before heading off to power lights and horn (like in the diagram you posted).
The black ignition coil is grounded to the case by the mounting bolts - needs to be clean and rust free on all contract points between the case the the metal on the coil.
Then make sure your spark plug lead is good - it screws into both the coil and the plug cap. Unscrew and chop off 10-20mm from either end and refit. Check continuity if you can, or just buy a foot or so of new lead for cheap peace of mind.
Are the points clean and actually opening/closing?
If all that doesn't work then it's probably the condenser (tin can looking thing) or the coil itself thats failed. Try replacing the condenser first - cheapest of the two.
Also are you sure it's not sparking? Sounds dumb, but I was sure I had no spark - couldn't see a thing resting the plug against the case. Then I turned it over with the plug lead disconnected and got a zap to my leg!
Hope I don't sound patronising, I'm no moped expert, but I spent a while trying to figure this stuff out for myself - all the US mopeds seem to have external coils, so the info in the wiki etc is a little confusing at first.