Hi. It seems you are quoting a line from one of my previous posts. I don’t know why on your Roku, the Apple TV app doesn’t seems to work. It does seems to work for many other Roku users. My conclusion from that is, that something about your setup or settings is likely different from theirs.
So, in that previous post I listed a couple of things to check that might be different. If you (or anyone else) never manually configured a firewall for your home that excluded specific servers, in some cases maybe excluding Apple servers, then that line does not apply to you. Some people like to tinker with that, and then that may get them in connectivity problems that could explain the described behavior.
If that previous post didn’t bring you clues for a better working app, then please ask the Apple Support staff what they can do for you.