Double run of 2 sets of speaker cables from stereo amp to single binding post speakers

It won't hurt anything so just try it. No one can say for sure what it will sound like, so that's the only way. 

Yup, I did it. Sounds nice, but no earth shattering difference to my ears.
Though much depends on your speaker/cable/amp interaction.

That type of wiring used to be called "shotgun" wiring.  Sometimes using a second set of identical wires in parallel with the first set is a nice improvement, but sometimes not.  I have a bi-wire pair of Audio Note SPx cables which have both + conductors connected to a single spade on the amp end and both -conductors connected to a single spade, and separate connectors on the speaker ends.  This allows me to try different configurations.  First up was true bi-wiring which I didn't particularly like with my speakers.  Next I tried a single pair of wires vs. a shotgun setup.  The shotgun had stronger bass which was nice but the midrange and treble were not as lively or realistic as the single pair of wires.  So there you go.  You just have to try it yourself and see whether you like the changes or not.

That's not what he's doing. Both his amp and speakers have just 1 set of binding posts. He's just connecting 2 different pairs of cables at the same time.

If you to do more experimenting, try running them in series so that the signal goes through the first pair of cables, and then the 2nd. I've never tried any of this, but I know people who have. They even claim they get a different sound running in series when you reverse positions. 

It gets cramped behind some of our cabinets and speakers.  Just make darn sure that you don't accidentally mix up the + and - leads on one end of one of the runs.  You won't like what happens.