The business is more than likely violating gambling regulations by soliciting US customers. IANAL, but Satoshi Dice did block US players due to legal concerns https://bitcointalk.org/index.php?topic=135521.0.
If there is a single Bitcoin mining node (out of thousands[0]) that will accept your transaction, you can play.
Correct. There is absolutely no way whatsoever to determine the originating IP address of a bitcoin transaction, short of global network surveillance.
IIRC Satoshi Dice worked by sending Bitcoin to a specific address for a bet and the address changed each time which they displayed on their website. By blocking US players from the website they could legally claim to be in compliance with the regulation (IANAL).
(IANAL)