Can I play for real money if I am not a permanent resident of New Jersey?
Yes, but only while you are physically located in New Jersey.
Once you leave New Jersey, you will no longer be able to play real money games if you are logged in under NJ.
You can browse the site and manage your account (including deposit, withdraw and set limits) anywhere in the USA, but you will only be able to wager while in the state of New Jersey.