Does EyeTV Sharing require other computers to be on the same network and subnet?

Yes. EyeTV Sharing requires all participants to be connected in the same network and subnet.

Make sure that all Macs are on the same network and share the same subnet. To make EyeTV Sharing work from a Mac with a wired network connection to a wireless network connection (or vice versa), your wireless base station should be set up to create a bridge between the wired and wireless networks.