That quote is not making a general statement that consonants after short vowels are geminated. It is instead saying only that *‑ni̯‑ > geminate -nn- after short vowels.
It makes no claim about the evolution of other consonants or consonant clusters. Strictly speaking it doesn't even make such a claim about short vowels other than *ă.
Note also that in the example given in the quote, there is no gemination of a single consonant, instead a cluster becomes a geminate.
Additionally, whilst it is common for languages to develop a restriction that all syllables be heavy (i.e. short vowels must be followed by a coda consonant), it's more typical for this to be done by lengthening vowels in open syllables than by geminating a following consonant (likewise it's more typical for a restriction against ultraheavy syllables to be realised by shortening long vowels in closed syllables than by losing coda consonants after long vowels).
It's actually this change (open syllable lengthening) and not the change you suggest (post-short vowel gemination) that occurred in Middle English.