You need covered space of about 4 sq. ft. per bird. That would be 4'x4' for 4 chickens (in the roost part). If they get out to free range during the day, the run part size isn't as much a problem.
That looks like chicken wire on the run. If you have predators, everyone says they can cut through chicken wire really easily. If you overlay hardware wire (maybe 1/2" squares) it will protect the birds better. In my chain link yard, I have chicken wire over the chain link on the outside edges of the yard and run. The coop is tight at night (locked door, hardware wire over the window openings), but we have raccoons and possums around here that would love a chicken dinner, not to mention the loose dogs in the area.
My hen hoop tractor was supposed to house up to 8 chickens. The internal coop part is only about 13 sq. feet (max 4 chickens and they would be crowded during winter storms when they are "cooped up"). I had to get my 7 girls bigger lodging before the winter. We had a tough winter, SO I'm really glad we did the upgrade for them.
Good luck with the chickies. You do have some space challenges.