It's "winnings are". It's incorrect to use "is" because the term "winnings" is a plural noun, and requires a plural verb.
It's "winnings are". It's incorrect to use "winnings is" because the term winnings is a plural noun, and requires a verb in the plural.
Her winnings are worth around 120 times the yearly earnings of a family.
Her winnings is worth around 120 times the yearly earnings of a family.
A partial list of other related plural nouns that also take a plural verb:
