"The news" is not from an Iranian source, thus not to be taken seriously.
As for the dogs in Islam, some of sunni and shia madhabs (jurisprudential sects) agree that they are considered impure. However, you are allowed to have them especially for reasons such as protection, hunting, etc. Taking them inside the houses in which humans live is impermissible. And even secular countries have this rule in apartments. And it is for reasons such as cleanness, noise, etc.
Personally I am against people having dogs in a neighbourhood, mainly because of noise. And I do not want people walking dogs in public either. My nieces are afraid of dogs, and I do not want them afraid when we have a walk.
There are other reasons people shouldn't have dogs. And I mainly think of the cost of having, feeding and taking care of one. When people could use that money for many other good reasons like sheltering an orphan or etc.
In any case, people can have dogs if they want. If they want dogs, they can have it. However, when it disturbs the people around, there has to be restrictions, like not having one in a neighbourhood or not walking them on the streets.
Well, it is not Islam Law, it is Iran's law.
Maybe you did not read the fact that even this Islamophobic-Iranophobic "source" does not claim that it is a law in Islamic Iran. It is not a law in Islamic Iran. The article says it is proposed and probably will not be accepted.