My dogs & cats are my family. I react the same to them being missing/not showing up at home as I would my child. It is a "NORMAL" reaction to anyone/pet that you have a close attachment with.
I own a small farm in the country & didn't realize that one of my dogs was blind & also had doggie dementia till she wandered off. I jumped in my truck & went looking for her. Found her wandering around a neighbors farm yard about 1/4 mile away after midnight. My pets are my family