No Java?
Seen as the readme says this in the very next sentence, and they reference Flash, I think they’re actually talking about the full fat Oracle Java runtime, not just Javascript.
Side note: I found a support page on speedtest.net that still says you need Flash installed, but only Flash, no Java required here: https://sandboxsupport.speedtest.net/hc/en-us/articles/202610754-What-are-the-requirements-to-use-Speedtest-net
JavaScript has nothing to do with Java. They are completely different languages and environments.
There were something called “Java applets” on the web before flash. It was real Java, probably a sunset of that. There was an addon just like flash.