Is there another black wire in the switch box? - Not any that provide the required return for the outlet.
I disconnected a stand-alone outlet for ease of testing. I had installed it a couple years ago directly below the light switch. I did a continuity check today to ensure that I was correct about it being just for that outlet.
Ding! Ding! Ding! Error!
There is more wiring in the switch electrical box than shown on the diagrams!
When making electrical diagrams, show ALL wiring please...
(So basically ignore what I said above. That was based on my thought that there were only two wires going to the switch electrical box as shown on the diagram...)
Do you show power on either of those black wires on the switch? It looks like that black wire that is connected to the reds run to the switch. The question is the other black on your switch: is it hot or does it run to the light? I still would expect 3 blacks at the switch box. The other possibility is the light gets fed from the last switched outlet (or one in between). In this case, you would have power coming in to the switch and then running to the 1st of the switched outlets.