"delete" in this article refers to the backspace key (← or ⌫) not the actual delete key (⌦).
So the combination your are searching for is ⌘ fn ⌫ or alternatively (if your keyboard has a number pad) ⌘ ⌦.
Note however that although these are system wide key commands, there are some 3rd-party applications that don't support them.
EDIT: The article also got some combinations wrong. It's ⌥ ⌫ for deleting the last word and ⌥ ⌦ or ⌥ fn ⌫ for deleting the next.
EDIT2:
It seems like ⌘ ⌦ and ⌘ fn ⌫ AREN'T system wide key commands (if that is a thing). They don't work in TextEdit or Pages BUT they do work in some other applications such as Apple's Xcode or TextWrangler.
Nonetheless you can achieve the same behaviour by using ⌘ ⇧ → (left arrow key) to select the text to the end of the line and then deleting it. This also works for words with ⌥ instead and for single characters with only ⇧.