By using all four screws on the receptacle you are wiring the circuit in a series. If one receptacle stops working then your whole circuit goes off.
Using all four screws still keeps the wires in "parallel" because the brass plate acts as a bus bar. In fact I cannot think of any ordinary way to wire them in series so that it would affect any outlets downstream. IF you broke the jumper out, you would have to install a shunt between the outlets to energize downstream devices. Then it would be in series and a failure of the shunt would shut down following devices, but NO COMPETENT, and few INCOMPETENT people would do it that way anyway.
Historically, series and parallel were used to describe how loads are wired relative to a power source. Unfortunately, overtime the words have been "laymenized" and lost most of their useful meaning. Series now has been dumbed down to mean a circuit where the current has one path, and parallel means a circuit with multiple current paths. Now, in typical AC applications these tell you nothing meaningful about the circuit.
Take for example the recp with the four screws wired for pass-through power by leaving the plate intact.
You argue its in "series" because the current has one path, if plug something in, it now has more than one path. Would it now be consider in parallel because the current has multiple paths?
What if the same receptacle is wired as part of a ring circuit, is it in series or in parallel?
What if the receptacle fails but still has pass-through power?
What is it if I just strip part of the wire (in the middle, without cutting the wire) and connect it to the screw on the receptacle?
Using this definition, a pigtail would be consider in "series", since the current has only one path (until you plug something in)?
In their current usage these words don't convey useful information and have corrupted their traditional meanings.