The issue was why use Onyomi here in the first place. Googling it is showing more hits for 食し・食す than I'd expected, though 食べる is obviously far more common.
Obviously 食べる has more widespread use, but that doesn't make 食する any less of a legitimate word. Literally meaning "to do food," it's just a more casual way of saying "to eat" as far as I can tell. Just as in English you might say "I'm going to eat" or "I'm going to grab some food" or "I'm going to have some grub" or "I'm going to chow down" etc.
Actually, my feeling for 食す is archaic/formal rather than casual. 食う(kuu) would be casual though. I'm writing this one off as a failed attempt by the artist to add depth to the dialogue that would be indicative of Rider's background / speech style. 食し方 is really unnatural sounding.
