The owb is meant to grip in one direction and spin freely going the other direction. That way it will grip to turn the engine over (like when you pull on the pullstart) and then when the engine is under it's own power, the owb can spin separate of the shaft (or vice versa) and not tear up the pullstart.
Sounds like Metalhead's got you going on the right track.
Have you tried removing the "hexagonal thing" from the engine by pulling it out?
Like Metalhead mentioned, clean it with some nitro cleaner, or denatured alcohol or fuel if you have nothing else.
I think you'll eventually want to pull the backplate, but until then if simply cleaning the owb gets it to grip and turn over the crank you're on your way.
Wait a second, I just now saw the video...
Is that the engine in question?
If so - that hex thing is the OWB.
You mentioned that when you turn the flywheel, the piston goes up and down.
When you turn the shaft on the other end, does the piston go up and down?
I can't really tell from the video.
If it does move, try cleaning the hex thing - or buy a new one - and make sure you install it so it catches in the right direction.
You'll want it to catch when you turn the owb clockwise and spin free going counter-clockwise.