I consider the reading order guide to be more like a suggestion. It shows which books are direct sequels to which other books, so you'll know to read the other book first, but technically apart from that you can read Discworld books in any order you want.

That said, I recommend reading them in the order they were published. Reading them by series (as in: all the Rincewind books, then all the Witches books, then all the Watch books, etc), is something I definitely do not recommend. There's a lot of cross-series references in Discworld, the chart is not 100% accurate, and you'll jump to and fro all over Discworld's timeline, which will get jarring.