I've just started learning WebGL+Three.js. Does anyone know how similar this pipeline is to how it is done in a browser? (and how much of this is still true 9 years later?...)
This being said, you can learn WebGL and especially Three.js without knowing the pipeline as described there, but knowing it will help you understand some subtleties or if you ever want to move to a lower level.
DirectX12 and Vulkan have changed the pipeline by making it more flexible, but still largely follow the vertex -> geometry -> pixel pipeline.
Because the DirectX11 (and OpenGL) immediate-mode pipelines were used for so long, I expect that for the DECADES to come, the information in this blog will remain relevant (even if more efficient techniques advance the state of the art).