Ironically I have been doing some research into wifi antennas these last few days, and I actually did see that, and immediately knew it was probably bullshit, because all of the elements and the reflector are connected together. Then, I actually saw a video with the same question you posed as the subject!

Lemme look it up.

TLDR, it's actually a type of yagi antenna, and while it technically might work, the "boom" isn't isolated from the reflector, essentially causing a short, which might just blow out your wifi.

The largest metal disk is the reflector, and it's attached to ground, the outer shielding of the coax, and the second disk, the boom, is attached to the center of the coax. You just gotta electrically isolate that disk, such as with heat shrink or plastic washers.

I'm not sure if the measurements are exactly right in the one you mentioned though. But, Andrew McNeil, who is the same one who did the video above that I linked, also did another video, where he adapted and simplified the design to be used in a "can", which results in an extremely powerful directional antenna.