The Oxford English Dictionary defines this word as “resembling Gnatho or his proceedings”. Next question, please.
Gnatho was a character in Eunuchus (the Eunuch), a play by the Roman writer Terence. He was the worst kind of flatterer, who would say black was white or yes meant no if it would please Thraso, the man to whom he has succeeded in attaching himself. The Latin word for him was parasitus, a parasite, a person who lives at the expense of somebody else and repays him with flattery (this is the original sense of parasite in English — the non-human sort came along a little later). The parasite in Greek and Roman literature was particularly fond of his food.
The word, and its older variation gnathonical, are defunct in English, though very occasionally resurrected to confuse the unwary at spelling bees with that silent initial g or by some writer who wishes to parade his erudition. The most recent example I can find of a genuine use is as far back as 1855, from Charles Kingsley’s novel Westward Ho!: “That Jack’s is somewhat of a gnathonic and parasitic soul, or stomach, all Bideford apple-women know.”
It is almost certain, considering the propensity of Roman writers to introduce puns, that Gnatho was named with a knowing nod towards the Greek gnathos, jaw, with reference to his consumption of the free meals that he obtained through his excessive flattery.