The comma indicates that what follows is additional information, not restrictive information. You can omit it without changing the meaning. It's a theatre. If the writer wanted to specify the particular theatre that is a stone's throw from his house, then the word the would be used and the comma omitted. Now, if there are several theatres, all a stone's throw from his house, more possibilities exist.
I subscribe to the usage that says the "comma indicates non-restrictive clause" and "no comma means restrictive". I pay less attention to the that/which distinction (mainly because I can't remember the logic of it!)