Why not let it output the gbuffer images instead, or perhaps even let it operate on the artwork instead? That way you could bake the changes into the game without having to run the NN in real time.
The image enhancement here is happening "in camera", like a fragment shader; but it's using a lot more context than the sort of local/cellular kernels that fragment shaders usually are.
Look at e.g. the gutters on the roads, where there are leaves/dirt — they get filled in with tons of extra perceptual texture (texture that exists in the projection plane, rather than texture that exists "on" the road), bringing them up to the same LoD as the rest of the road.
If that texture was "pushed back" to the origin texture, said texture would have to exist at some sort of ridiculous resolution that modern graphics cards wouldn't have a hope of rendering.
So, rather than rendering the road at 8x-16x and then downsampling it, in order to get a pile of leaves to appear to have ~1.5x LoD at the projection plane, you can just achieve that 1.5x LoD pixel by pixel at the projection plane.
Or, to put that another way: when a digital artist is painting a landscape, they don't have to zoom in by 8x, paint every individual blade of grass, and then zoom out. They can just use an artistic technique at 1x zoom that approximates the texture that would have been created by downsampling "photographic" detail painted in at 8x to your screen resolution.
Here, the ML model is playing the role of the digital artist, "painting" on the projection plane.
To do that, you’d need access to the game’s source code and assets, and you would need to rewrite portions of the rendering engine. Training might be incredibly slow if it needs to iterate on builds of the game, or that problem could be worked around but might need considerable engineering to support the training iterations (e.g. data representation and a pipeline with the ability to render changes to the artwork and renderer on the fly without needing a game rebuild).
So I’d speculate the answer to why not is that it’s just not what the authors set out to do, that they don’t have access to the game source nor the time or resources needed to refactor the renderer.
Part of the magic of neural networks is their black box properties - they can do what they do without needing to understand 3d geometry or integrate with a render engine. Throw an image in, and a new image pops out, without the neural network needing to understand what it’s doing or why.
That said, I would guess that coming down the road is examples of exactly what you’re suggesting - games that will use neural networks to drive realism in the assets and shaders and renderer. To some degree there are already tools starting to do this.