This article focusses mainly on pairing by classification. Here are a few other things to consider when pairing fonts:
X-height: This is the height of the lowercase "x" glyph. You will notice that there is an imaginary line around where many lowercase letters line up at. This usually falls around the crossbar of an uppercase "A" and "H". Finding fonts with similar x-heights helps make a nice match.
Glyph width: Finding fonts with very similar widths or very contrasting widths is also something to consider. If they are somewhere in between, it sometimes feels weird.
Taking these attributes into consideration, in addition to their Era/Classification/Style really help in pairing fonts.
I guess this article assumes you know how to pick a single typeface.
Hoefler & Co does a great job of demonstrating their techniques for pairing fonts. (albeit a bit non web app biased)
https://www.typography.com/techniques/
Keep in mind that serif typefaces do not always render pleasingly to the eye as they need more pixels to render correctly. These pixels are needed to render the subtle serifs. Monospace and sans typefaces suffer a lot less from this problem.
It is one of the reasons I never advise to use serif fonts for text body. Nowadays, betterresolutions are used more often, but low res displays are still common enough.
As stated in the second paragraph, this is "simple method to pair typefaces." Traditional typefaces have complex extant cultural connotations. Some of these are nationalistic. Rules of thumb regarding shapes are useful, but you combine letterforms outside their historical context and previous application at your peril.
X-height: This is the height of the lowercase "x" glyph. You will notice that there is an imaginary line around where many lowercase letters line up at. This usually falls around the crossbar of an uppercase "A" and "H". Finding fonts with similar x-heights helps make a nice match.
Glyph width: Finding fonts with very similar widths or very contrasting widths is also something to consider. If they are somewhere in between, it sometimes feels weird.
Taking these attributes into consideration, in addition to their Era/Classification/Style really help in pairing fonts.