The legend tells that years ago every casino in Las Vegas had a three-piece chicken dinner with a potato and a veggie for $1.79. A standard bet back then was $2, hence when you won a bet you had enough for a chicken dinner. !”
Man: "I'll give it a shot!" (throws hardball style, hits and knocks down the jugs)
Carny: "Winner Winner Chicken Dinner!" (hands man a Chinese made stuffed animal)
Individuals, or teams would gather on Wednesday evenings and Saturday mornings, to shoot clay pigeons.
The team and or winner would win a frozen chicken(s) (meat shoot) to take home to eat...... the announcer or competitor would yell out "winner winner chicken dinner"
Likely the insult originates from the term's common use as it relates to a "cheap win" in Vegas.