I don't know if it's meant to be a joke, per se. They use (or used) the Unicorn server once upon a time:

https://github.blog/news-insights/unicorn/

https://news.ycombinator.com/item?id=4957986

I don't think it's a joke, it's the server that github runs on

https://en.wikipedia.org/wiki/Unicorn_(web_server)

Even if it is their server name, I completely agree with your point. The image is not appropriate when your multi-billion revenue service is yet again failing to meet even a basic level of reliability, preventing people from doing their jobs and generally causing stress and bad feeling all round.

One of Reddit's cutesy error pages (presumably for Internal Server Error is similar) is an illustration that says "You broke reddit". I know it's a joke, but have wondered what effect that might have on a particularly anxiety-prone person who takes it literally and thinks they've done something that's taken the site down and inconvenienced millions of other people. Seems a bit dodgy for a mainstream site to assume all of its users have the dev knowledge to identify a joking accusation.

That stupid "Aww, Snap!" message I think it's one of the browsers does.

I am personally totally fine with it but I see your point. Github is a bit too big for often braking with a cutsey error message even if it is a reference to their web server.