They have around 100 images on a single page, and google analytics increases the 50 bytes with 1KB. This does indeed result in 100kb overhead
What the thread OP is talking about is the decrease in page size from the URLs included in the page source. Choosing a shorter URL for the static domain versus a longer one resulted in a rough savings of 50 bytes per page (size), compressed.
You're referring to request cookie size, which was also decreased significantly (CloudFlare still sets a single cookie, unfortunately), which results in the big savings of ~100 KB upstream per page load.