Actually this makes perfect sense to me, having worked in the casino, and seen some of the children's devices in "ticket arcades" albiet not the ones at Chuck E Cheese in paticular, the similarities are uncanny.
The whole first floor of "The Treehouse" Arcade at Foxwoods Resort Casino was full of these kinds of things when I worked there. I didn't play them of course so can't say for sure, but I did see a lot of people playing them.
I'll also say that even when it comes to "games of skill" I think they tend to be rigged to a degree where it comes down to luck anyway, even if there is a more active component to them. It depends on what your talking about though.
To put it bluntly for the arcade to stay in business, more money has to be spent on the games than the value of prizes that are handed out. What's more your typical arcade has to maintain a pretty high volume of business, and this means having a lot of kids who are going to go there to hang out constantly. If kids can develop skills through practice to actually come out ahead regularly, the whole thing would collapse.
Now at a casino it's one thing, despite the agreements with the state that kids won't gamble, you can kind of say "duh" but those machines are mass produced, not created right there. Your typical boardwalk arcade is doubtlessly doing things that if more money was involved along with more lavish prizes would probably be considered criminal.
It's also telling that if some kid goes to get dad, or his brother who shoots hoops, they typically can't come out ahead on things like basketball shooting games, at least not reliably. After all if all your typical kid had to do was go get his big brother who lives on a basketball blacktop to win the big prizes the arcades would also go out of business, so all illusions of skill mattering aside... it really doesn't all that much.
The level this is argueing on is harmless, but I see the lady's point, and yeah... I really can't defend it even if my instict is to label her a whack job. Sad to say it, but I think she should win this one.