حَضْرَمَوْتُ: two words fused into one proper name - تركيب cause applies.
عَبْدُ اللَّهِ: idafah - this تركيب cause does not apply.
جَاءَ زَيْدٌ: a sentence - this تركيب cause does not apply.
The question is not “Are there two words?” but “Have they become one compound proper name?”