The best way to be certain is simply to trace it all out. Those are good photos, but that is a tough job to trace it out from an arm chair
But I think your hand drawn schematic will work just fine. I would just add an input resistor (experiment), starting with 10k and 2k and see which works best for you. If you wire this according to the schematic that you drew, you won't go wrong.
This is a very simple opamp circuit. I may look daunting to a beginner because of the number of parts involved. But most of those are simply there to provide the virtual ground (provide the opamp with a split power supply from a single battery).