In the US, a common formulation is "anything of value." So whether you're betting dollars, doughnuts, or tea-cakes, it comes under the law. The authorities aren't necessarily very consistent about enforcement, though. An example is a children's restaurant chain, Chuck E. Cheese's, which runs blatant games of chance offering prizes of value. There is no way this is legal, at least in jurisdictions that ban other games of chance run for profit, but you don't see the police knocking down their doors. This is pretty silly, considering that if the addictive potential of gambling is why it's banned, it's utterly absurd to let children gamble. It would be like banning cigarettes for adults, but then ignoring cigarettes marketed directly to children.
(Not that I think either is a good idea.)
They got Capone on Tax Evasion - when they can't arrest you for one law they will find something else.
If they want to shutdown a Bitcoin site that hasn't broken any other laws, they will apply it selectively here even though they don't apply it to Chuck E Cheese. After all, Chuck E Cheese has lawyers, lobbyists and friends in government and we do not.