Speaking of an “extended passport validity rule” may be confusing things. This is no separate rule, rather third-country citizens are required to hold a valid travel document to enter the Schengen area. This document must also meet two additional requirements:
- its validity shall extend at least three months after the intended date of departure from the territory of the Member States. […]
- it shall have been issued within the previous 10 years;
By contrast, EU citizens do not require a passport to enter or live in the EU, they can visit other EU countries with almost no restriction, and can reside indefinitely in another EU country (i.e. there is no “intended date of departure” to consider) so it's obvious that none of this does or could concern them.
The EU freedom of movement directive, which the Schengen Borders code explicitly references, also makes additional arbitrary restrictions illegal. EU citizens can indeed enter any other EU country as long as they hold a valid document.
Incidentally, as noted in a comment and detailed in Why do passport validity rules exist?, these rules exist to facilitate force returns, which are exceedingly rare and almost impossible for EU citizens residing in another EU country.