In our cities today, this is already true. There are areas where prices are very high and poorer people can't afford to buy houses there. The same thing would apply for this 'dome city' too.
The article says "may be free to wander through by day, but they will surely find no residence there"; just like our current divide of richer areas vs poorer areas.
Then the article says "It won't be long before there will be those who will be desperate to get inside; and it means an authority will be established to decide who can, and who can't."
Why do you need that? Free market economy will control the prices of housing in the dome just like our current housing rates as per school district lines or proximity to other valuable services.
I don't see how this is any different from our current rich/poor housing divide.