Follow z to g, then b to f, through this spice’s spellings.
Latin zingiber became Medieval Latin gingiber, which English borrowed as gingifer. Middle English altered that form on the way to ginger. Small changes at the beginning and middle hide a long borrowing history.
The cards select four forms, omitting Greek and Middle English as separate steps. The Pali relative cited by the dictionary is not treated as a direct donor.
Source
Merriam-Webster: gingerWord History supplies the successive forms and distinguishes the Pali relative from the borrowing route.