Personally, I don't believe it should be legal at all. In Australia and NZ, where I'm from, they just won't let you in until you're 18 and (I believe) 20 respectively.
Allowing kids to play, and then funneling the earnings through their parents with extreme tax consequences is the kind of bizarre middle ground I'm not surprised to see from the US.
Well, it's not really allowed in the US either. Minors aren't allowed on the gambling floor, but Keno games can be played from essentially anywhere, such as the restaurant where you take your family to eat. A "it's legal if you pay extra" loophole doesn't exist except to the extent that if you lie and put the wrong name on the form, it's hard to check.
Allowing kids to play, and then funneling the earnings through their parents with extreme tax consequences is the kind of bizarre middle ground I'm not surprised to see from the US.