No, no water polo or family barbecue.
Rome is a series which is almost entirely about the power struggle in Rome. As a matter of fact, that is how it is described. "A struggle between the common people and the nobility. Two soldiers, one who would make himself king."
There are scenes of characters sleeping, eating, working, walking, praying, playing the harp, showering, singing, picnicking, and otherwise doing things people do.
You see the seeds of war being sown within the palace, but you also see how it affects the people.
People are starving. Ooh look, a character who is starving. Jews are being treated badly. Ooh look, a Jew who has been treated badly.
It's really not difficult to work these things into a show, especially when the source material probably describes everything about these places and their inhabitants in tremendous detail.