Is my engine falling off? Help..

There's an ongoing problem of bad shaking/rattling during cold starts. Often if the day before you happened to start up and shut down right away. There was a service bulletin, I think some people got replacement intake manifolds mod'd in some manner. Maybe didn't improve things though?

Try to avoid the above scenario, always let the engine warm up, never shut down a few seconds after cold start, and see how it goes.

That's hands-down the funniest thread title I've seen here, btw.

 

how many miles on her?

 

That is weird.
When I had the "misfire and shake on start-up" occur after just starting the car to move it into the driveway the night before, the engine shook rather noticeably. I watched the video twice and did not see the engine noticeably shaking. Furthermore, the sound is not quite the same as what my engine sounded like when misfiring--your engine sounds like something is slapping while mine sounded more like a light banging or rattling. So I am puzzled.
Do you have an automobile mechanics stethoscope ? It is a doctor's stethoscope with a long metal rod replacing the usual small cone that the doctor puts on your chest to listen for sounds. Use that metal rod to poke firmly onto various metal bits on the ICE and any surrounding gizmos like air pumps, hydraulic pumps, or whatever. The sound should become louder as you get closer to where it if coming from, and become piercingly loud when you actually probe the piece causing the noise . Knowing which physical piece is the main source of the noise while help us figure out what in the world is causing that particular sound.
Good luck!