I agree. We need to understand if there is a single winding with taps or multiple windings.
If two wires are shorted by the switch then they should measure zero ohms between them (or as low as the ohmmeter can go). Can't both be on one winding or it would make a shorted winding.
I'm guessing there are two primary windings with taps, in parallel will be 110V and 120V, in series will be 220V and 240V. The question is which wire belongs to which winding.
Probably the slide switch on the right selects the small transformer input voltage.
https://manualslib.com pioneer vsx605s pdf
https://manualslib.com pioneer vsx605s pdf
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I just found a transformer schematic for the VSX453/SDXJ, maybe it will provide some help.
https://audiocircuit.dk/Pioneer-VSX463S-avr-sm.pdf
If the VSX605 has the similar connection, then the blue wire is not the screen and seems like it is connected to AC input.
https://audiocircuit.dk/Pioneer-VSX463S-avr-sm.pdf
If the VSX605 has the similar connection, then the blue wire is not the screen and seems like it is connected to AC input.