Yep, definitely not new tech. (You probably know this next bit, but just for anyone scrolling by).
Having your server verify every action is the only way to prevent hackers from simply sending a packet that says "I got a headshot on that guy". Instead the server replays through all their actions. You never say you got a headshot, you just say when you clicked and the server figures out if you hit.
And because like you mention, clients only receive gameplay data and not the fully rendered screen, this allows clients to do things like interpolate the (delayed) server data with their own realtime input elements. Otherwise every single action you take would be delayed by whatever your latency is, and every other player's actions would be delayed by a similar amount. Instead, it appears seamless until your latency gets so bad that you just begin teleporting between positions because the server can't track you well enough (often called multiplayer rubber-banding).
Instead (well designed) game servers run their own authoritative version of the game world and track each player's latency, and use that to replay the previous few ticks of the game when an input comes in from any player. So if you have a 100ms ping, and press "W" to walk forward, when the server receives your forward input it treats it as if you have been moving for 100ms already.
Basically, saying every player shares the world model is incorrect unless you can set them all to the same latency.
https://developer.valvesoftware.com/wiki/Lag_compensation
https://developer.valvesoftware.com/wiki/Latency_Compensatin...
Edit: additional source, these gafferongames articles are a bit old (2004) but still extremely relevant.
https://gafferongames.com/post/networked_physics_2004/
https://gafferongames.com/post/what_every_programmer_needs_t...