You don't need a battery but you'll want a battery.
Yeah, looks a bit of a basket case that bike and you're asking us to make wild guesses when it could be anything.
You've not running a snorkel, that engine does not sound crisp at all, you can tell it's swamped with air and it's struggling.
Without a battery you're relying on the generator making sufficient power to do all the lights and make 20'000 volts at the spark plug lead, coupled with the poor wiring, bad earths and the second rate coil, it's no wonder it's not running right.
You need to get yourself a battery.
Sort the wiring out
Get a genuine coil on there
Get a genuine snorkel fitted
https://ebay.io/m/cHVjjv
Make sure you got good grounding from the chasis to the negative terminals.
Search on this forum for the wiring diagrams as there are many different grounding points, different for different years, so ensuring you got the wiring for your model will ensure you capture the grounding points.
Ultimately there is not a lot to these engines, but you have to have the basics done right, otherwise we're stating into the abyss trying to help you.
