To post pictures directly to the discussion thread you need to be a contributor for 12 bucks a year. In the meantime you can add some to your "Gallery" and "Garage" functions in the User CP above.
Or like some do, use an online hosting site like SuperMotors if you're going to be posting pics across the internet to various other sites.
First of all, normally the voltage regulator would not cause the engine to run rough. But in your case, it's not even bolted down or completely connected, so you should NOT be running the engine until you bolt that thing down.
Second, nothing should be touching the business end of the ignition coil where the HT lead comes out, because under some circumstances it could be jumping spark to ground, which would indeed cause your engine to run like crapola.
Third, your coil should not really be mounted there, but that's not really the end of the world with a well manufactured coil.
We need a pic of your alternator. Perhaps it was converted to an internally regulated version and the external voltage regulator is no longer needed. We can tell at a glance (usually) what alternator you have.
If it still needs the external regulator, you can fry them by applying power before it's grounded. If you're going to have that problem, it's probably already happened.
Hard to tell even from the video, but it looks like you're having a fueling issue because I could see the throttle lever moving and nothing happening until just before the video cut off and you were able to rev the engine.
Kind of like the choke is closing too far, then opening up just enough for it to run. But by the picture from that far away, it does look like the choke is partially open still. So that might not be the issue.
But if your "fueling issue" is really an ignition issue (they get mixed up a lot) then we're not sure yet until more testing is done.
Paul