The expression is a humorous way of describing a competition involving imaginary ducks in a game. There may be a possibility of word play involving a well-known vulgar word which rhymes with 'duck', often followed by 'off' in a rude expression meaning 'go away at once!'.
Often a verb, noun, or phrase ending in 'off' is used when some kind of finality is being expressed.
A number of idioms related to competitions, (sporting or otherwise, e.g. elections) have an -off suffix. For example, where two candidates in a election have an equal number of votes, a 'run-off' or 'runoff' is held. In these contexts, a 'something off' is a activity which decides a winner.
: a final race, contest, or election to decide an earlier one that has
not resulted in a decision in favor of any one competitor.
—used for a public contest for amateur cooks in which contestants must
prepare and bake their entries within a stated time
less commonly play-off
: a final contest, series of contests, or period of play to determine
the winner between contestants or teams that have tied
(All Merriam-Webster Dictionary)