Internet Gambling Regulation and Tax Enforcement Act of 2008 - Amends the Internal Revenue Code to: (1) impose an Internet gambling license fee on Internet gambling operators; (2) require such operators to file informational returns identifying themselves and the individuals placing wagers with them; (3) require withholding of tax on annual Internet gambling winnings of more than $5,000; (4) impose a 30% tax on the Internet gambling winnings of nonresident aliens; and (5) impose the excise tax on wagers on any individual who places a wager with an unlicensed Internet gambling operator.