If you read the article, it says they didn't do Anything except force them to do energy efficient and safe housing upgrades. So Denmark actually failed.
Looks like they passed a law designed to curtail speculation and rapid price hikes throughout the country. It says landlords cannot raise rent on apartments they renovated for 5 years after they purchased them. They must increase energy efficiency too. Finally, they cannot pay tenants money to leave.
Maybe it will help some. Time will tell.