For the casinos themselves, there's no doubt that it would be illegal to operate their business in the US.
For the player, things aren't nearly as clear.
Some states have passed laws regarding it, but there is no Federal legislation that applies. The Justice Department claims that the Federal Wire Act applies, but on three separate occasions this question has been challenged in court, and all three times the courts have ruled that the Wire Act does not apply to casino-style gambling. (It mentions betting on sports events.)
Every year, a few members of Congress propose legislation to prohibit Internet gambling, but every time so far, the efforts have been defeated. This year, there's a fresh assault. We'll see how it goes.
It is amazing to me that the US is willing to give up all the potential tax revenue that regulation instead of prohibition would provide. And most industry experts think that regulation is inevitable, as prohibition can't possibly work. The question is how many years of offshore revenue are lost before the US Congress comes around.