I dunno, I tend to think of increasing the total number of pixels as being an increase in the resolution, even if it's only to change the FOV.
For example, I think of going from 1920x1080 to 1920x1200 as an increase in resolution, because there are more pixels. If the game happens to be Vert- and just so happens to increase the FOV with this change, then I guess that would be incidental in my mind to the more visceral act of increasing the pixels/resolution. I guess, usually in games, you adjust the actual resolution by changing the pixels, and the FOV is not usually something you interact with directly, but rather just arises based on the change in resolution.
But I haven't played much of the newer games, are they letting you do a slider to FOV adjustments? that would be pretty cool; I remember doing some kind of hack to let me adjust FOV dynamically while playing Bioshock 1 (I was using SoftTH on triple monitor back then, the hack let you press Function keys to increase or decrease horizontal FOV) and it was kind of "trippy" like a rubber band, but definitely changed what the computer displayed on screen to where I guess the CPU had to render more or less stuff depending on the FOV. But usually, I just change the pixels/resolution and the FOV is not something I choose.
Well you're right, FOV changes when aspect ratio changes, all due to a change in screen resolution is purely incidental.
It is worth noting that monitors are obviously fixed aspect ratios and to make proper use of the screen space of your monitor any resolution you pick ideally should be the same aspect ratio anyway. You could argue that unless you're switching monitors or dumb enough to pick an inappropriate aspect ratio, the aspect ratio should remain the same as you increase or decrease the screen resolution.
FOV has been tweakable in many engines ever since 3D rendering, it used to be set reasonably high for PC games back in the day and exposure of the FOV was often only through develop consoles or ini/cfg tweaks. Modern games tend to use very small FOVs because they're basically console ports and console games tend to use low FOVs for several shitty reasons, this had lead to complaints on the PC platform and more recently the exposure of FOV controls in the video settings of some modern games like BF3.
Remember the CPU isn't rendering anything it's mostly doing calculations on things like game states, AI, physics and alike. However some of these game assets are often destroyed or switch to simplified behaviour in the engine when they leave your visibility, for performance reasons.
For example once a car or pedestrian in GTA goes out of your visibility by some predetermined amount then it will eventually be destroyed or at least simplified, they don't simulate peds and cars for the entire city, only some small subset of that total area, highly likely this subset is at least partially based on the players visibility, along with various other rules probably.
Increasing FOV does also increase art assets in the scene as well and can cause more load on the GPU for similar reasons, but the percentage increase in load the additional FOV causes on both the CPU and GPU respectively is likely to be different and in some cases it could be enough to flip the previous bottleneck from one to the other. Depends entirely on the game and circumstance at the time.