As the features on this website date from the early 2000s, you will need to use a browser from then as well. Luckily, one is very secure. (It doesn't seem like there are any installers for Mac, sadly.)
This obscure browser is by far the safest and most convenient way to use this website. It is built off the Firefox engine, but plugins such as Adobe Flash and Shockwave Player aren't disabled. They even work right out of the box as you install it, no settings need to be changed. (UPDATE: If the Phase 1 lobby doesn't seem to load, change the security settings to not force HTTPS.)Download Pale Moon (choose the 32-bit version.)
Here are the recommended installers in case you removed them. They are hosted on archive.org which takes legitimacy very seriously.