So I guess back to basics:
> A streaming media service, also known as streaming service, is an online provider that allows users to watch or listen to content, such as films, TV series, music, or podcasts, over the Internet
Fairly simple, I think at least. So with that, is what Sony is doing a streaming service, regardless of what HBO/Amazon/their mother is doing? Yes, in my humble opinion, what Sony is offering lets users "watch or listen to content, such as films, TV series, music, or podcasts, over the Internet", so it is a streaming service.
I disagree it's pedantic, it's just understanding what terms mean, in this particular case, what "streaming service" means.
Every “streaming service” is a distributor. Some of them are also content producers.
Content production is also a bizarre mini world of VC-type funding and shell/temporary production corporations. Some companies lean heavily into that, some do a more traditional in-house studio model, some do both.