I'm not sure what people mean when they say "So-and-so is not ham radio", but I don't think they always mean the same thing. First off, saying that something is not ham radio is in no way a criticism of that thing or of the people who use it. Dentistry is not ham radio, but that's consistent with the fact that, when you have a toothache, you should go see a dentist. In my personal opinion, things like echolink and (internet assisted) d-star are not ham radio, but that does not imply that people shouldn't use them and enjoy them. I myself use d-star on a regular basis. I am not the least bit perturbed by my belief that it is something other than ham radio because, whatever it is, it's a convenient way to chat with some folks. Why should I care, or even be particularly interested in, whether it is ham radio? If I enjoy it, I enjoy it. Describe it however you like.
Or more to the point: Why should you care what somebody on the internet thinks of the technology you decide to use?
All of those things you mentioned above are indeed "ham radio". Tunnelling communications through the internet is not. I'm a big fan of digital modes myself, which are generated at my QTH and transmitted via a small amount of RF to arrive at it's destination and then hopefully solicit a reply. I can see the use for internet tunneled communications for emergency communications, but it really isn't any more ham radio than chinwagging on a Discord server. I don't need thousands of dollars worth of radio and antenna gear or a licence to do that though. Why even buy a radio?
Why? Because you don't like the idea? Plenty of people said FM repeaters weren't ham radio. "How can that be ham radio? Your signal is tunneling through another transmitter and being rebroadcast!" Ham radio is what hams do.
