Dolphin isn't reading 3D models, they're just tweaking the matrices that the game sends. Increased resolution sort of similar the same -- the game sends the hardware triangles in an abstract model space, which is converted to clip space (where the left of the screen is -1.0 and the right is 1.0). Increasing the resolution just means adjusting the rest of the transform; everything the game sends is in abstract space.
(Yes, I know there's a bit more to it than that, e.g. virtual XFBs, LOD biases, and so forth)
Basically, unlike the PS2, the GameCube is pretty much an ancestor of modern PC GPUs, so its way of doing graphics is very familiar to us, and maps quite well. And this is not an accident! ATI bought the company that made the GameCube's GPU (ArtX), and put out a GPU so good (the r300) that NVIDIA nearly went out of business.
Also, fun, I ran into the same "GLES doesn't support glReadPixels for depth" when working on the lens flare code for Wind Waker and Super Mario Galaxy in https://noclip.website. Had to do some dirty tricks to convert it to a color format first.
I was lucky with drivers but I heard a lot of horror stories so also switched to NVIDIA when I finally got around to upgrading.
The R300/Radeon 9700 (based on the ArtX IP) came out late summer of 2002, and several months later NVidia launched the dismal GeForce FX series (which is the project that most of the 3DFX “rampage” team went to work on after acquisition). The fundamental problem with NVIDIA’s design was that it was optimized for 16-bit precision pixel shaders, and then-new DirectX 9’s “pixel shader 2.0” model mandated a 24-bit minimum precision. The R300 ran FP24 math natively, and consequently ran circles around the FX series in DX9 performance.
NVidia didn’t really catch up to and surpass ATI until much, much later.
I agree ATI still dominated Nvidia in sales well into the 00's, Nvidia took a long time to offer competitive cards. The solder issues & Cap Plague didn't help them any, either.
edit: just watched a video and I am completely sold
"Free Look is a longstanding Dolphin feature that allows the user to reposition the camera in a game however they so please, with abilities far far beyond what game cameras can provide. This allows for exploring blocked off areas, advanced game photography, and more. "