The Doctor could just be referring to Whale in the same way The Stranger referred to August.
Could Whale be a greek god? They’ve already included Midas so they’re not avoiding greek mythology.
Maybe Hades, lord of the underworld?- As a doctor, his decisions could make the difference between life and death. He’d be a god therefore he would have “a god complex”. “Frames himself a victor in all conflicts”- death always wins- nobody can beat death.
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Keeper of Felix