I touched upon this, but honestly this is a very, very large subject that requires familiarity with the Berne Convention and TRIPS/ACTA in order to fully explain.
In the Canadian decision, the de-listing order is contingent on that order not being contrary to compliance requirements elsewhere in the world. However, the SCC doesn't have knowledge of all of those laws, nor should it. Accordingly, it stated the burden upon showing a contradiction rests with the applicant, Google, who didn't want to comply with the order. Google would need to cite specific laws they were in contravention of, rather than just pleading that there may, maybe, somehow be a contradictory requirement. What if there wasn't? Should Google still get to plead international comity in that instance? No.
Positive freedom of speech legislation might work as an alternate requirement, but this was not plead, and this was not a situation where the speech in question is political or particularly protected. It is a very clear instance where a supplier has fled Canada (and they can't find where they're based) in order to attempt to continue crystal clear trademark violations which are causing actual damage to a Canadian business.
The current international trademark framework means that the majority of nations in the world would actually require compliance with this order (well, not exactly, but close enough). The big question is how that machinery should be activated. If the Respondent had the money to pursue passing-off litigation in every jurisdiction, they would likely arrive at a similar result, but functionally, a small company won't be able to pay x200+ times the legal fees for a similar result while their dealflow is being sapped.
This decision, even read very broadly, wouldn't provide countries with the ability to de-index items. Countries don't need that ability; they already have it. Most, however, have bound themselves not to exercise it, but certain, like China, actively pursue control as an overt element of their policy agenda.
I feel like I'm doing a bit of a disservice to the topic, because there is a lot of small nobs and levers that I can't get into without exploding this into a 20 page memorandum. I am confident in stating that the freedom of speech concerns arising from this case are not as dire as portrayed.
Edit: Made the middle a bit clearer.