Sure you can, it's just called WebGL! ;)
They just added another layer, flipped the words "server" and "client" around, and added more hardware.
Now you run the web browser client on top of the local window system server, through shared memory, without using the network. And both the browser and GPU are locally programmable!
And then the local web browser client accesses remote web servers over the network, instead of ever using X11's networking ability.
One way of looking at it in the X11 sense is that a remote app running in the web server acts as a client of the local window server's display and GPU hardware, by downloading JavaScript code to run in the web browser (acting as a programmable middleman near the display), and also shader code to run in the window server's GPU.
Trying to pigeonhole practices like distributed network and GPU programming into simplistic dichotomies like "client/server," or partition user interface programming into holy trinities like "model/view/controller," just oversimplifies reality and unnecessarily limits designs.