...but the object of the game was to shop for dinner, but by only taking stuff out of other peoples carts...
Just for ***** and giggles, I asked our local district attorney if there was any type of crime here (in case I wanted to scare my wife and/or kids), and she said, "No, but if they were taking things out of the cart that a person had an expectation to have purchased, it
may be considered Criminal Mischief (which in Oregon means to create an inconvenience)"
So in other words, if a person puts something in their cart, then goes to the checkout counter, buys their stuff, gets home, finds it isn't there, has to return to the store for it, and it creates a substantial enough inconvenience, the person causing the inconvenience could be found guilty of Criminal Mischief III.
The way my kids are doing it (especially considering they don't use perishables), there is no risk of that.