In عَبْدُ اللَّهِ, there is an iḍāfah: عَبْدُ is the first term and اللَّهِ is the genitive second term.
In قَامَ زَيْدٌ, there is predication: an action is attributed to Zayd.
In بَعْلَبَكّ, two elements combine into a single proper name, rather than an ordinary genitive phrase.
When applying the book’s definition, first rule out a normal iḍāfah or predicative relationship. These comparisons are added teaching examples.