Aha! Sneaky.
Ok, there is an important difference from the video. The cap pops off, but it has two clips, and a spring not a button.
Working toward the rear, you need to pop off the right side of the round cap on the left-hand post. This requires releasing two clips, then rotating the cap up and left as in the first photo.
The second photo shows what's revealed, with the spring pulled out. Flip the seat forward and pull the headrest out.
The third photo shows the spring back in (note the flat side to the left, and the curved side becoming the return spring for the button that's not actually there). The orange arrow shows the tab which engages the slot, do this before snapping the cap back down.
Finally, the result in the rearview mirror!
You could probably flip the spring over (or leave it out altogether) so the headrest can plug in and out without ever going back in there... But it might be a little wiggly.