I don't see how this video shows anything which supports your .. fears? Obviously, you shouldn't short-circuit capacitors. You shouldn't short-circuit any power source.
Where would you get the high-amp power supply though?
It doesn't have to be a high-amp power supply- you could use a low-amp supply to charge up another supercapacitor, then use that capacitor to charge your laptop's supercapacitor.
the best thing about supercapacitors is that they don't have a liquid inside. It means that (at least theoretically) they can be of any form and thickness. So, (again, speculatively speaking) they can be a part of laptop frame.
> they don't have a liquid inside
They do:
"...electrolyte (an ionic liquid called EBIMF 1 M)..."
My fault. I thought they use the approach described in [1], where the prototype used LightScribe DVD optical drive to make a pattern on a disk with graphite oxide film. That prototype didn't require any liquid.