You can combine that with the fact that the shelter in question has limited capacity and euthanized 20% of animals in the last year. Roll a 6 sided die, and on a 6 your pet dies. That is absolutely a threat to kill pets.
Read to the bottom, where they specify that they have rated this as "false" because "The city did not threaten to kill any pets 'as punishment.'" The city merely said that they would give your pets to a shelter that kills 1/5 of the animals it takes in - a shelter that kills pets for "extreme fear" which could include separation anxiety from the pet's owner. They don't explicitly say that they are doing this to punish people because they don't say why they are doing it.
Also, make no mistake, nobody is going to outright say "I will kill your pets if you don't leave," but they are going to make threats like this that provide them with some plausible deniability to say "we didn't actually threaten to kill your pet, the shelter was just overwhelmed and couldn't take it."
I see no reference to any particular shelter in that tweet, nor do I see a citation to support a 20% kill rate.
EDIT:
Based on that source, the Humane Society had a kill rate of 20.6% in that year. Of those 10% were due to "due to serious behavioral issues such as aggression and/or extreme fear". So, a kill rate of 2.6% excluding health and/or owner request. That's not really a coin toss -- that's the Humane Society making a judgement call on whether a pet can be rehabilitated. I have no insight into the Humane Society's decision making here, but this number is clearly in the minority.
I don't think the government is being unreasonable here or threatening the wholesale slaughter of animals. They're asking people who have brought their pets to a protest to be responsible pet owners and find a safe place for their pets before the police move in, which is the same thing they wanted responsible parents to do with their children.
Let's assume we're talking about dogs here, unless people are bringing their really extraordinary cats to the protest. Anecdotally, in the GTA it can really hard to adopt a dog. One shelter I tried a couple of years ago didn't have a single dog. As a pet owner I would see the greater threat here that my dog would be taken from me and adopted out to a new family. In Ontario, euthanasia wouldn't be my first concern if I were to lose a dog.
Citation needed.