The ruling was that this was a hate crime, because it was "menacing, anti-Semitic and racist". I have trouble seeing how a Nazi pug that responds to "gas the jews" is anything other than silly bit of absurd comedy. I can't realistically see this video actually advancing any legitimate hatred, or having any negative consequences other than some people laughing at how silly it is, and some people just thinking it's kind of stupid.
For what it's worth, I grew up in a town that was roughly half jewish, reflected in my circle of friends. When I was younger, extremely crass jokes that made light of historical tragedies were made at everyones expense, including ones that historically affected my family. It was clear that the intent of these was not to instill terror or provoke hatred. It was more of a pissing contest, to see who could say the most absurdly offensive thing.
Were these the types of situations where we should have had more sensitivity to the real weight of these tragedies? Sure.
Were these hate crimes? Absolutely not. When someone commits a hate crime against you, you probably wouldn't regularly invite them over to your house for the next several years...
That's curious given your background. I know a couple of people that still have the tattoos on their arms and one guy who literally has no family at all and it pains me to see that people think that this is just a matter of bad taste. "Gas the Jews" is not a joke, my sense of humor is pretty broad but it does not stretch that far.
I can't even count the number of comedy central stand-up specials I've seen that casually make jokes about absolutely horrific things that destroy lives. Jokes that play on children dying, slavery, the holocaust, rape, murder, pedophilia, torture, etc. I guarantee you that both you and I both know someone (or are one person removed, at most) that has had their lives destroyed by one of these things, or something of a similar caliber. Does that mean that none if these jokes can be funny, in any context? If so, I'd say you'd be hard pressed to find a single comedy special that counts as funny; virtually every comedy special I've seen makes light of one of these horrific things in some way.
I think you're simply appealing to emotion here to justify an unjust ruling and an unjust law.
I think the person you're replying to has a point in saying that some laws in Europe are pretty ridiculous. However, the difference is that that's a local law in the UK and not one that affects the entirety of Europe. Nor is it a widespread law in other European countries.
And fwiw I do think Europe is oversensitive about Nazis-related stuff. But for good reasons.