Why are these binaries called kernels? Is it at all related to a kernel in the context of OS's?

To quote Kayvon and David from class, kernel is used here to represent a side effect free function that gets executed inside a larger algorithm.

Don't think the kernel here refers to OS kernel. Folks usually use the word "kernel", to refer to the core or most important part of something e.g. OS kernel, Database kernel etc.

I think kernel is related the fact that GPUs are made for performant image processing, and a common image processing task is a applying a convolution matrix (called a kernel) to an image.