I can confirm that it is the Apple Watch that is downloading the update from the Internet, over Wi-Fi. This explains why it has to be connected to a Wi-Fi network to initiate the update; it's no longer the iPhone that does the download and then pushes it out to the watch.
For the record, I initiated the update on my iPhone, and 172.16.10.213 is my watch's IPv4 address on my home network (no OpSec risk in revealing my home's internal IPv4 address space, since it is shared by thousands of other networks per RFC1918 criteria).