Isn't this exactly how Doom worked, long before Serious Sam?
But Quake went a different direction, sending the client updates about every entity they could see. Which had some benefits (players don't have to be perfectly synchronized) but also drawbacks (bandwidth proportional to scene complexity).
This is covered at the very end of the article, in the "Comparison with Doom and Quake" section. And yes, that's exactly the comparison and distinction the author draws, and they explain why Serious Sam would have opted for Doom-style networking (the notoriously high scene complexity).
But Quake went a different direction, sending the client updates about every entity they could see. Which had some benefits (players don't have to be perfectly synchronized) but also drawbacks (bandwidth proportional to scene complexity).