The headline is misleading. These are not "public" places. They are private property in many cases. I don't know if Scotland has ever been strong on property rights.
I added the additional title descriptor about the ban applying to public places because that's the way it's referred to in the body of the article. Even though a given venue may be privately owned, they are nevertheless regarded as public places when they are open to public ACCESS. It's the same here in the US...privately ownned bars and restaurants are regarded as 'public places'.
That being said, I agree with your sentiment that this is an infringement upon rights, both those of the property owners as well as that of the patrons. The property rights angle is one of the ways that smoking bans are being fought here in the US.