The dogs only crime was being too curious and big enough to be perceived as a serious threat to the baby deer. The Doe's reaction was not unjustified since the dog is the same as a wolf and a wolf would have been a real danger to the baby. For that matter, so would many dogs though not necessarily this one.
The cat was seen as a less of a threat because of his small size but the Doe did turn on him when he continued to press. Cats are territorial just like dogs and they can express it by bullying other animals like that.
Bingo.
About a minute into the video you can even see the fawn reacting to what probably looks like a wolf to it. It feels threatened and drops to the ground trying to be as flat and motionless as as possible. Then its mother goes after that poor doggie, but at least it survived.
Also, I'd like to add that the cat ran like hell as soon as it realized its scare tactics were futile and that it was about to be stomped into the grass by something that was easily 8 to 10 times its size, doing anything other than that would only have left it stupid and dead.

