Yes, not having the entire game state on the user's computer in the first place is a solid choice. And for many games, that's exactly how multiplayer works. They run all the logic on a server, "never trust the client" (that is, validate all the input that clients send to the server), and only send data the user needs to know.
However for something like an RTS, the amount of data in game state updates can be prohibitively large to transmit to clients. The deterministic lockstep networking model described in the article is a solution to that problem. In that system, the only data transmitted is input, and each client updates locally, so it does require them to have a copy of the entire game state.
However for something like an RTS, the amount of data in game state updates can be prohibitively large to transmit to clients. The deterministic lockstep networking model described in the article is a solution to that problem. In that system, the only data transmitted is input, and each client updates locally, so it does require them to have a copy of the entire game state.