Different OSes have different fonts installed. If a web site uses a font that isn't installed on the system the web browser is running on and doesn't specifically download it as part of the CSS, the browser will attempt to guess, choosing the locally installed font that it thinks is "closest" to the font requested. Sometimes there isn't a good match; other times, the browser simply guesses badly. The end result can range from a page that looks subtly different, to a page layout train wreck (if the site is relying on specific font metrics).
A similar thing can happen if the site does not use an explicit font, but makes incorrect assumptions about the properties of the font the web browser defaults to.
The New York Times web site rendered really badly on my Linux desktop for a couple of weeks recently (seems OK now). I've seen similar issues on other mainstream sites over the years. So this issue can affect even high-profile sites.
The site you linked looks OK to me (Chrome on Ubuntu Linux), but I don't know what it is supposed to look like so I have no basis for comparison.
Edit: There's a weird effect being applied to the fixed top navigation bar, where the horizontal/vertical spacing of some elements changes slightly depending on whether you've scrolled down the page or not. Not sure what the point of that is, as it adds no functionality to the page. Egregious "stupid CSS/JavaScript tricks" are a pet peeve.