What’s the benefit of placing speakers like this? (diagonally at the corner)

millercarbon...Did you try what is in the link you posted? If you did, what was the result in your opinion? 

One big reason is the enhanced depth of the soundstage.

As mentioned the reduction of early reflections is probably the biggest reason.

With Roger Sanders Flat faced direct radiating electrostats ( Still the best sound I have ever
heard) he explains that the more asymmetrically placed you set his speakers up,
the better they sound. Ask him if you're a doubter. 

I have two larger box speakers in a 14 x 16 room open on opposite ends to other spaces.
I tried the four different "Standard" configurations that one would use. The best was the one
with the an open space behind me.

Then I thought -WTF, let's see about a diagonal setup. Yes it was much improved that way.

Get some help before moving all that heavy gear around!!!

I use this setup in my listening room.  Did it mostly for interior design benefits given my furniture, windows, fireplace, but things sound spacious and echo free.  https://systems.audiogon.com/systems/9074

I think  my current listening space in my hexagonal shaped bedroom has pretty much the same effect as the setup in the Vinnie Rossi article. I chose to treat the 1st order reflection coming from a short wall next to my left speaker, but otherwise the room seems to naturally sound great. Compared to the square or rectangular rooms that I've previously had, this room sounds exceptionally quiet. I can that tell there are few if any stray reverberations mainly because I don't hear the echoes that I just unconsciously thought were present in all rooms.

The primary reason is much smoother bass as the standing waves are not allowed to multiply as much as in a rectangular or square room.
Best,
Jim Smith