I still want to know what "human emotions" are in the first place. Exactly where along the evolutionary chain did we suddenly pop up with these special things that all other animals somehow missed out on?
Perhaps contemplative wonder?
I understand where you're coming from though. I find a universality between the intensity of when empathy is shown to me by my family, my friends, and my dog.
Does he speak words? No. But sometimes neither do the humans in my life for me to feel empathy being given to me.
Case in point, I go through my spells of grieving every now and then since my grandmother died. I'll sit down on the couch, and our dog has noticed if my sitting carries with it a certain heaviness, that I'm thinking of grandma and shed a tear or two. He usually jumps up onto the couch and sits next to me. But when I'm grieving, I've found him on more than one occasion jumping up, sniffing my face, licking my cheek, nudging my arm to rest on his back, and then he lies down next to me resting his chin on my leg. Every now and then, he sniffs the skin on my hand or sits up to sniff my face again, licks again, and nudges my arm again until it's resting on his back.
He doesn't do that unless I'm upset. It's comforting and sweet, and I feel companionship with him when he does sniff, nudge, lick, and cuddle. Even if we are two completely different species.