This is correct. Amazon Prime Channel includes live HBO. HBO NOW does not. For some inexplicable reason, HBO NOW which has the word NOW in its name does not include what is on HBO right now.Okay since there seems to be some confusion, if you sub to HBO through Amazon Prime Video you get to watch the live linear channels in the Prime Video app just as on cable/satellite with the Eastern feeds of all the channels + HBO West. However, you can also use your Prime Video credentials in the HBO Now app, so it's not either/or. If you sub with Prime Video (as I did) you get the best of both worlds, live AND on demand streaming.
One other thing to add. The HBO live feed really is just live. There is no record buffer meaning you can't pause it to get a drink or run to the toilet. You had better be sitting on your butt in front of the TV exactly when the show begins and not move a muscle. This trade off really is the tragedy on losing HBO on the Hopper.