I guess a house can be a home, but house is incorrect here because the context implies something more than simply a structure of a house?
So for clarification, это acts as a subject ("This is") and этот is more like an adjective ("This _ is")?
That would be more like, "Это мой город, мой дом". The Russian isn't saying that this place is both my city and my home, it's saying that this city, этот город, is my home, мой дом.
I thought that after posting (considering 'мой' only appears once), but thank you for confirming.
You need to forget the fact that your house is not a city but in the city