I can't speak for this specific model/extension, but "most" neural networks aren't that big at the end of the day, and you are just a few matrix dot products away from getting your classification (of course, I'm drastically simplifying).
Its the training that takes forever, due to the fact all those numbers need tweaking. However one you have the model, classifying is pretty fast.
Yes, tensorflow model can run on JS. I did that when developing a Deep Learning product, PredictSalary (https://predictsalary.com). The problem is not the model, but the TensorflowJS library (using Node) is big (8MB) after webpack-ing it (even after using compressing flag).
So I decided to move the inference to the server.
It's fast but I didn't toy with GPU setting when running Tensorflow model on JS.
Would it be feasible to run the model in wasm or in the GPU?