I don't have the book so I can't directly reference the circuit that you are referring to, but here's how I determine parallel vs series. After going through element 1, if you must go through element 2 in order to come back to element 1, then they are in series. Another way of saying this is that if you must go through both elements to go around a full loop, then they are in series.
This doesn't by itself mean that the two elements that are not in series are in parallel. Rather, element 1 might be parallel to a combination of multiple elements connected in series. If you can go from point 1 to point 2 in a circuit by either going through element 1 or element 2, then they are in parallel. Conversely, element 1 can be in series with a combination of multiple elements that are parallel themselves. That is, after passing through element 1, you have to pass through either element 2, 3, 4, or etc., but not more than one of them. Hope that helped.
