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.