I don't see how this is driver's fault. But it is very sad, yes. It boils down to whether the driver took "reasonable" care.
The video also states a neighbor claimed the driver "tossed" the package over the gate. I watched the video - it didn't look like tossing to me.

Drop before hitting the ground? That's irresponsible for something weighing anything more than a pound or two.

What an ass why didn’t he go to the front door?

I don't see where he "threw" it over. Theft is a huge problem anymore and you can't leave this stuff on the front porch in some
areas. I think the driver was trying to prevent theft. They're on such a tight schedule and they don'thave time to ring and wait.

He is supposed to "deliver" the package. He was taking a shortcut to save himself time and effort. Tossing the package over a fence could have resulted in damage to the contents or damage to the owners property. (sprinkler heads, vegetation etc.) In this case it killed a pet. The guy should be fired and UPS should be sued. I had a postal worker do the same thing. Tossed a package over our fence into a wet area on the lawn. The package was soaked after sitting there for a while. I called the postmaster for my area and complained. I doubt my call was the one that did it but that guy was gone a few weeks later. Theft prevention has nothing to do with it.

I realize these are two different situations, but are very congruent. My wife and I quit taking our late Cairn when we flew. The last time he was shipped, it took him half an hour to quit shaking after we picked him up. Because of completely erroneous info on his pickup, after a 20 minute wait at the carousel, we found out that he was not going to be taken off with baggage. By the time we found out, we had to race to a car rental to get a car to make the trek to the freight terminal. If we had been 15 minutes later, he would have spent the night alone in a crate, unwalked and unfed.

After that, any time we were considering travel, we all either went in the car, paid a sitter a smell fortune, or one of us stayed home. If you love your pets, find an alternative way of getting them there, or stay home.

The dog wasn't IN the package. The idiot lazy delivery guy dropped the 55 pound package ON the dog killing it.

My bad. I had not watched it at all, preferring to NOT see a poor wee dog being so badly hurt.

Now, I cannot be sure which is worse - this, or the misapprehension under which I was operating. Definitely a far worse action by the courier. How could any sentient human do that?