The author is working on piet-gpu, a library for efficiently rendering 2D graphics on the GPU, for UIs and font editors and things like that. This is very nontrivial (and in fact most 2D graphics you see today are in large part rendered on the CPU).

The goal of piet-gpu is that you just specify the scene graph (blue circle here, red line there, etc) and send it over to the GPU, and the GPU takes care of all the rendering.

GPUs are very good at processing data in the shape of arrays. For example, a pixel shader (or "fragment shader") processes a 2D array of pixels on the screen. piet-gpu needs to sometimes process data that has a tree structure, rather than an array structure, to support clipping (for example to show a shape that represents the intersection between a circle and a square). The stack monoid the article talks about is a way of doing tree-like operations in parallel on the GPU, and the author thinks it will end up being useful for being able to process clipping operations entirely on the GPU.