The promotion, like it was done in the US, UK and other parts of the World, was meant for subscribers of it's Premium service to receive a Google Home Mini for free. Subscribers of the Family Plan (which pays $5 / month MORE), were not included as Spotify considers this to be a "discounted" membership because 5 people can be on a single account.
After some backlash, Spotify decided to offer this promotion to Family Plans ... well, except when it came to Canada. Canada had the same backlash, but I guess since they're a smaller country, they just don't matter as much.
Spotify Chat Support offered a solution:
Jonah P: Not to worry, we have a work around for you. Jonah P: 1. Cancel your current Premium for Family subscription at https://www.spotify.com/account/. 2. Wait for your account to revert to Free at the end of your billing period. You can see when this is on your subscription page: https://www.spotify.com/account/subscription/. 3. Then, subscribe to Spotify Premium at http://www.spotify.com/premium/ to get the Google Home Mini. 4. Before your current paid month expires, upgrade your account to Premium for Family at https://www.spotify.com/family/.
Unfortunately, that didn't work either for most people, since by the time their subscription renewal period came through, they had ended the promotion. So, not only did they not get the Google Mini, they also pissed off everyone on the Family Plan since all the saved songs were gone!
So far, the only response seen from @SpotifyCares regarding this issue is to repeat that this promotion is only available to Premium Subscribers. It has yet to be seen why they offered this promotion to Family Subscribers in other countries and not Canada.