You are corrent that the resolution increase mainly affects the GPU performance. However, most texture streaming algorithms calculate the needed texture mip levels precisely (using screen space texel density). 1080p will stream 44% more texture data from the hard drive compared to 900p. If the texture data is stored in a compressed format not directly supported by the GPU (such as zlib, lzx, jpg-xr, etc), that data needs to be uncompressed (or transcoded) during loading. This step takes some CPU time (as variable length data decoding is often processed on CPU). Obviously 1080p also need 44% memory to store the texture streaming working set.
If you are using virtual texturing, 1080p will generate approx 44% more page requests compared to 900p. This means that the page management requires a little bit more CPU time. Depending on what operations are needed to be done when a page is generated, this might actually cost some real CPU cycles. For example in our case we render lots of decal triangles to the virtual texture pages, and this means more CPU work to setup the draw calls. On modern GPUs (with compute shaders) you can offload most of this work to GPU (if you prefer to do that).
Some engines also use screen size based LOD system (swap LODs by pixel count) to maintaining the same geometry density per pixel on all resolutions. This means that the triangle count depends on the screen resolution. This is mostly an extra GPU cost, but if the last LOD is visible for further distance when the resolution is higher, it also means that the CPU must setup more draw calls and cull more objects.
These real world examples show that some engines incur a (small) extra CPU cost when the resolution is increased. I don't know anything about this particular case however.
