How do I add an Apple TV to hotel wifi without a browser?
Use a computer to imitate or “spoof the MAC address” and register the AppleTV hardware address and agree to the terms is the pragmatic manner to join. 

Unlike the post you found, however, it can be done much more easily with a MacBook and without much jujitsu.


First get the MAC address of the Apple TV (available in Settings) and shut it down.
Then run the following in Mac's terminal app, replacing the MAC address shown with that of your Apple TV: sudo ifconfig en0 ether 98:01:a7:a1:f6:77.
Next confirm the change by running ifconfig en0 | grep ether.
Finally use your Mac's browser to sign-in and bypass the captive portal.


Once that's done disconnect or power off your Mac, plug your Apple TV back in and connect to the network as usual. Instructions here summarized from Spoofing IoT Device MAC Addresses.