"To connect the UniFi Travel Router to a guest network, open the UniFi Mobile App and select a nearby wireless network. If the network has a captive portal, it will automatically forward to your mobile device for login."

from the FAQ https://store.ui.com/us/en/products/utr

It likely relies on the travel router cloning the MAC address of your phone or whatever you use to authenticate. That way the hotel just thinks the travel router is your phone.