Well, it looks to me like the hex socket in the screw is just rounded off, not thread or shank damage at all. If so you are in luck as what could have been a 5od of a job just got a lot easier. So, the 50K$ question. Is the problem that allen key is just spinning in the destroyed hex hole, or is the black part that immediately surrounds the hole turning with the allen key and the problem is below??
If its a rounded hex in the screw, you could whack in a torx bit as the video suggested, but you may be able to get by with a conveniently sized flat blade screwdriver whacked in - that would be the first thing I'd try, even if you have to file the screwdriver blade to make it a suitable size. An old timers dodge for this type of job was to whack in the tang of a file, by the way. Basically, anything whacked in that you can use to apply torque. As was mentioned earlier this thread, that screw should not have much torque on it.
Alternatively, if you have a dremel, or know somebody who has one, with an appropriate cutter you could machine in a slot that a screwdriver could engage with.
And if it is just a rounded hex socket, drilling it out becomes much more feasible as it won't spin.
For completeness, I should mention a clever little bu99er called an easyout
https://en.wikipedia.org/wiki/Screw_extractor
Graham
PS this may appear in duplicate as it didn't post the first time.