Times is really not adapted for the web and is particularly bad on low-resolution screens. How many computer terminals used Times for anything but Word processing?
Verdana was released in 1996 — is that too recent?
Also, the website styles don't specify font-family at all, so you are complaining about your own browser defaults.
Good pickup on the font being the default browser choice, I didn't notice that!
But that's not true at all! Maybe the point was that web should use sans-serif instead of serif, but that statement (and I hope I'm not making a straw man here) is as a blanket invalid as well (in my opinion, ofc).