Out of curiosity I created a small demo detailing how you can implement GZIP in the browser, I used
fflate for the GZIP compression, and
pretty-bytes to convert bytes into human readable format, the demo is really small but as an example it should be more than good enough. I based it on bundlejs.com. Interestingly, I have yet to find a website that lets you see the GZIP size of some random text, all the ones I have found so far expect you to upload a file, the little demo takes a string as an input compresses it, and gives you the final size.
Codepen demo: codepen.io/okikio/pen/ExmQwPM
I suggest checking out bundlejs.com it's a specialized for bundling, minifying and compressing js, all locally, right on your browser.
Check out the product hunt page for bundlejs.com,