I think it’s silly and misinformed to suggest that animals don’t have emotions. Granted, they’re likely simpler and not the same kind of wide range that we have, plus, of course, they have a limited range of expression. I’ve studied animals, taken animal behavior, spent hours observing them and taking notes, all of that. I can tell you that my scientific-spidey sense tells me quite clearly that animals do feel things, from happiness, to fondness (if not love), joy, fear, anger, playfulness.. and that’s at the very least. Here is a source to back me up.
To answer the original question, I definitely do. I notice huge behavior changes in my cat when I’m gone for even 5 or 6 hours at a time, which means there’s an interruption in our normal routine, where I’m around most of the time. When I’m here and hanging out, the door is open and she goes out for 1–3 hours at a time with no thought to me because she knows I’m home. When I am gone for several hours and I come back, she is far more clingy and chooses to hang out inside with me rather than go out.
I was apart from her for 3 months this summer, the longest separation we’ve ever had. She had loads of stimulation, love, great care, and everyone loves her. She had toys, affection, and acres of land to wander around. It should have been like summer camp!
When I went to pick her up after I got back, she was gaunt. She had plenty of food and water (in fact, her caretakers wanted to spoil her), but she still lost weight. She was obviously miffed at me for having been gone for so long and when I first arrived, she kind of acted like she didn’t know me, quite the opposite of the ‘running across the field toward each other in a cinematic reunion’ fantasy I’d had about seeing her again. Instead, she gave me the cold shoulder for a while, but went nuts over my flip-flops and acted like a freak, rubbing all over them.
Anyway, I’ve been back a couple of months and Kali’s filled out again, back to her normal, healthy weight. So, yes, I’d say she missed me.