Yes, you can search for FITE in the Android TV app store. Just install the app and then log in with your FITE email and password. Your purchase will sync automatically.
Important: At this point in time Facebook log in cannot be used on Android TV. You have to reset your password from https://www.fite.tv/account/login/ and enter your Facebook email. Use the new password to sign in.
If your purchase does not show and you are logged in with the correct account please restart the FITE TV app and start it again. This will refresh your purchase list.