A game mode can be patented because the code might be innovative and unique enough that it presents an edge in the gaming market while a genre is any form of communication that has socially agreed upon conventions developed over time. For example, Walt Disney could have patented several innovative animation techniques for, and I am not making this up, drawling Bubbles in the Dance of the Hours sequence from the 1940 film Fantasia (the one with the Hippos and the Crocodiles). Rather he opted to destroy all the filming rigs and technical notes from the films production and the actual "How did they do this" was believed thought lost to time to animators and historians alike. If it wasn't for the collection of private notes taken by animator Herman Schultheis now known as "The Lost Notebook" and 2014, nobody would have been able to reproduce bubbles of this quality (animators focus on really small details. Anyone can draw a bubble... nobody for nearly 3/4ths of a century could draw them like Walt Disney studios did. I once listened the director commentary of The Muppet's Christmas Carol where the director said that one of the most complicated scenes Jim Henson's studios ever filmed was filmed for this movie. The scene in question, was a few moments during a musical interlude in the One More Sleep til Christmas Sequence where Kermit closed a door and turns a key to lock it. Apparently it's difficult in Puppetry to do that.).
Had Walt Disney opted to patent the bubble animation technique, he would have been able to control who used it and how it was used for about 20 years... but he would have had to reveal the secrets to everyone.
Conversely, Fantasia's genre cannot be patented because, while probably a genre first, you cannot prevent people from making films that are edited to fit pre-existing music. Could you imagine a world where MTV couldn't broadcast music videos? Why, I bet it would be nothing but vapid dumping ground for reality shows about people with too much money and not enough sense, am I right?
Similarly in coding, the studios that can patent game modes, probably are writing some new code to do something unique and new in the gaming world. But that doesn't mean they have sole exclusive control for 20 years over genre conventions be it story telling (Post Apocalyptic fiction wasn't Last of Us's gift to the world, nor was Survival Horror (I think that's what it's narrative and game genres are... never played and barely know anything about)).
