ضَرَبْتُ أَنَا وَزَيْدٌ: no separator, so anā reinforces the attached subject.
ضَرَبْتُ الْيَوْمَ وَزَيْدٌ: al-yawma intervenes, so reinforcement is not needed in the book’s example.
In both, Zaydun is nominative because it is coordinated with the subject pronoun.