Recommended Approach: Add via IT Support
You don't need to setup your own router, you just need to contact the network's tech support and have them manually add your device via MAC address.
Large chain hotels use companies like Innflux to deliver HSIA and manage their networks. Typically, these companies will allow you to connect your device to their network, but you must go through them directly. You simply need to contact their customer service number, and give them the hexadecimal MAC address for the piece of hardware you're trying to connect.
The MAC address is a unique, factory-set identifier and it's usually printed on the bottom of the hardware or on the box it came in. It looks something like
AC:3A:6B:BE:B7:C1. If the device has a user interface, you can often get it from a network settings area.
The network technical support phone number is often printed on a card explaining internet access around a guest room's desk. Otherwise, ask a staff member at the front desk for it.
If your device connects to their WiFi network, but doesn't have internet access, you can also copy down the assigned IP address to give to them if you don't know the MAC address.
These companies setup network architecture and use techniques like port isolation to increase wireless network security for their clients. Port isolation prevents connected devices from communicating with each other directly.
Alternative Approach: MAC Spoofing
In theory, you should be able to connect your Apple TV to the network by spoofing its MAC address on your laptop, and connecting that device to the network before swapping it out with the Apple TV. This alternative approach may be against your particular service provider's policy and is likely frowned upon. I recommend using the aforementioned first approach, but if you're curious, I created a walkthrough for those willing to try this. Spoofing the MAC on my laptop and connecting that way has worked for me multiple times.