Looks like it was built with ASP.NET MVC 4, which has minification and bundling built in. Should be easy for them to take advantage of it... maybe they just ran out of time or don't care.
We recently moved to GitHub Enterprise and it really is not as expensive as it looks. It is $250/year per developer... not really that much considering what you get. Plus it is a virtual server provided for us, so we just have to upload software upgrade packages to get the latest updates. We didn't have to spend the money on someone to set up all of the MySql, Redis, Solr, etc. services to get it running. So honestly I consider GitHub Enterprise to be quite a cost savings. Just a counterpoint...
EDIT: We are not a startup, but still something to consider.
I know you say that in jest, but I would say that it is still good to know the underlying technology. It is much easier to debug issues in the future once you understand them.
This is actually referenced in the article. You can use the Last-Modified date and the server will either return a 304 (Not Modified) or the modified image if it is newer.
This is why we use QA servers for most of our systems. We try our best to test all functionality on a patched QA server before deploying patches to our production servers. We have had good success doing this (with Windows at least.)