Thanks for posting the video.
Based on the video, the antenna at the side of the right joy-con, next to the battery, does look like a NFC antenna. From the earlier photo, I thot it's a metal piece but in this video, with it actually taken out, it's a PCB, not metal, and is generally how NFC antenna looks like. Odd that they placed it at the side rather than flat under the NFC reader.
Unfortunately the video does not cover anything that looks like wireless communication method (be it bluetooth, FM etc.), so it doesn't give us a clue on the actual chip used in the joy-cons to communicate with a docked Switch or communicate with each other (if it's actually doing so). The Broadcom chip he mentioned seems to be NFC, unless NFC is just an add on function, when it's main duty is Bluetooth. (If that's indeed the Bluetooth chip too, that could mean the antenna is serving dual duty. Or the Bluetooth chip on the left joy-con could be a different chip, one without NFC.)
The problem with the video is that he only opened the right joy-con, so he doesn't compare the difference. For example, he couldn't find the HD rumble stuff. The only remaining device inside that could be for the rumble is that white block at the bottom. But since he did not open the left joy-con and see that the white block exists there too, he probably thot it's the IR sensor and ignored it.