According to the Apple TV manual: http://manuals.info.apple.com/en_US/Apple_TV_2nd_gen_Setup_Guide.pdf the AppleTV does use IP addresses, and is set up to automatically get the IP address from your router (via DHCP). There's an onscreen menu that gets you to this configuration page.

IP addresses aren't required for all communication across the internet. TCP/IP is the most commonly used protocol, especially for web use, so it's most familiar.

If your router just needs the MAC address (which all ethernet devices must have and use) to grant connection privileges, you can often look that up on a sticker on the bottom of the network device (Apple TV in this case) and manually enter the 12 character value.