I would say private server is more what you’re referring to, also CIG’s wording, but maybe agree to disagree. A quick search says that they haven’t cancelled that feature, but it’ll appropriately be the very last thing they work on
the common understanding of “dedicated server” is a server binary you can download and run yourself. a “private server” is usually still hosted on the company’s hardware.
I can understand you have different criteria for dedicated servers, but private servers are certainly not generally characterized by still being on 1st party hardware. You need only look at private servers for Minecraft, WoW, and the like
minecraft server binaries are a prime example of a “dedicated server”. tf2 is another. the alternative is a “listen server”, where one player acts as server. note that the term’s use in gaming has very little to do with the concept of a dedicated server in general use, aka a machine dedicated to running a service. in multiplayer games a dedicated server is just the name for a binary that contains no client.
anyway, the important distinction is whether the means for the game to continue existing is in the hands of the players or the company.