Do GPUs re-draw a all of a character's vertices/triangles/fragments every frame?

What you've said is how most games work, at least at a logical level. (In practice, these stages might not happen exactly sequentially - a GPU might be simultaneously drawing some fragments while rasterizing others and transforming vertices for the wave of triangles after that, and a mobile tile-based GPU might work on one tile at a time rather than rasterizing all triangles of the model at once. But the net effect is the same as if those stages happened in exactly that order.)

It's entirely possible for a game to implement on-demand rendering, where the code waits until something changes, and then asks the GPU to draw a new frame only when a change happens (or, to be even more selective, only re-drawing the part of the screen where something changed).

In practice though, lots of games have things changing all the time, even if it's something as simple as background/idle animations, so there's little benefit to implementing this kind of selective rendering. This is especially true in 3D games, where anytime the camera is moving, just about every pixel on the screen will change. The camera tends to move a lot during gameplay, so we need the process of re-drawing every pixel to be fast enough to happen every frame if we want to keep that motion smooth. If we've already made it fast enough to do every frame, then we might as well do it every frame, even if it's not strictly necessary, rather than add extra complications into our code to save that work. It's already part of our frame budget, so we might as well spend it.

The only real downside is when running off of battery, where those redundant frames will drain the battery faster than caching one image until it needs to change. So, if you're making a game targeted for mobile devices where lots of time is spent on screens where little to nothing changes, then in that case it might pay off to implement that logic to re-use frames when nothing is changing.

For most modern 3D games running on modern hardware, you've described the basics of how rendering usually works. However, that's not the only option. Other options include:

• Using Mesh Shaders instead of vertex shaders.
• Doing the vertex processing on the CPU.
• Fixed function hardware.
• Not using meshes that consist of vertices and polygons (e.g. voxels, implict surfaces).

So, to answer your final question: No. It doesn't happen the way you described in every game. As an example Doom doesn't work that way.

EDIT: For reference, the main differences in Doom from what you described are:

1. It's all software rendered (at least in the original PC version), so there aren't really any vertex shaders or pixel shaders.
2. The characters are all rendered as billboards (i.e. 2D sprites). This is a very common technique, for example it's also used to render the characters in Mario Kart 64.