A website can be composed of a bunch of files that your browser downloads and then renders to what you see on your device.
One common type of file contains javascript code (aka js assets), which can sometimes be relatively large, like several megabytes (MB). If a website gets hit by a lot of users, those MBs add up, and can chew through the bandwidth allotted for the given website. Consuming more bandwidth can cost more money for the website operator, who pays a hosting company for the website’s resources (disk space, compute time, network bandwidth).
To help alleviate this, and to also make these downloads faster around the world, Content Distribution Networks(CDN) exist. The idea is that you upload your large files to the CDN, have your website link to the CDN for big files, and now browsers pull big files from the CDN when the website is loaded instead of the website’s host itself. However, contracting with a CDN costs money too, just maybe not as much as a web host charges for hitting bandwidth overages.
Another important component to note: archive.org is a non-profit that in part has a web crawler whose entire purpose is to periodically take a snapshot of every website on the internet. This isn’t just a screen cap of each website either, it’s a copy of all of the files that actually compose the website. This is an oversimplification, but is good enough for the concluding example that follows.
So back to the case in the OP. What the dev did, was choose not to pay for and utilize a CDN to link to, but rather used archive.org’s copy of large file(s) to link to. So when a user loads the website, all of the bandwidth hogging files are being served for free from archive.org. But it’s really not free from archive.org’s perspective, since they’re the ones ultimately paying for the bandwidth.