The Austrian law you're quoting isn't a law sitting all by itself. It's part of a law saying "No Nazis, and no bullshitting about what they did"[1]. If you look at your own quote, you'll see it says "grossly plays down". The scale of the Holocaust was large - there was a heap of physical evidence, and tens of thousands of eyewitnesses. And it's not a topic that has had little research - to characterise the story of the holocaust as springing forth from the mouths of politicians is grossly misleading.
Denying the holocaust altogether is not research - it's an attempt to stifle research for political gains. It moves the needle from 'what actually happened' to 'did it happen at all', wasting resources - the same needle-moving tactics are seen in intelligent-design and anti-climate-change arguments, stopping productive conversation on a topic to further a political goal.
Finally, note that these laws limiting freedom of speech around holocaust denial are particular to that topic and nazism. The 'slippery slope' argument hasn't taken hold; it's not these laws that are limiting freedom of speech (hell, even with "the American concept of free speech" you still have Free Speech Zones, National Security Letters, and copyright that lasts for author's life + 70 years). The laws don't stop you from doing research into the shitty things the Allies did. They don't stop you researching Nazism in general or the Holocaust in particular. They only stop you playing politics from pretending that something does't exist when it has tens of thousands of eye-witnesses, troves of physical evidence, and heavy existing research on the topic.
Europe has a problem with violent nationalism; cutting off this particular avenue helps alleviate that, and doesn't do harm in return. These laws make Nazism (and it's trappings) less able to be used politically, something Europe is serious about - see Merkel's recent chiding of Netanyahu for him claiming that it was Palestinians who started the holocaust. How often do you see a head of government declare "Those atrocities, they're on us, not anyone else"?
[1]https://translate.google.com/translate?sl=de&tl=en&js=y&prev... (does not have section 3h, added in '92)