One of the patches involved is called 'autoaim'. How will the server know that the human user didn't actually aim that precisely?

That's a good first step but it doesn't really stop hackers. Specifically the two cheats that the parent mentions don't require the server to trust the client. There's mitigation that can be done to prevent wallhacks, but aimbot can be really difficult to detect without sophisticated tools, and even then fundamentally the cheat can operate as an intermediary between mouse input and the game receiving that mouse input which makes it impossible to directly detect without memory inspection. Essentially you're left with heuristic analysis of mouse movements, or more likely a "Overwatch" (CS:GO) type system where moderators/janitors are tasked with evaluating players to determine if they're cheating or not.

We don't really have the technology to do that completely. Because it's really hard and expensive to stream pre-rendered video at a low enough latency, most action games still transmit player positions and trust the client to accurately render the corresponding video client-side.

Although, even in scenario with a completely untrusted client receiving only final video output, there's no guarantee that the actions being input are human.