BILOXI, Miss. — This seaside gambling resort along a stretch of the Gulf Coast, sometimes called the “redneck Riviera,” has 40 percent fewer hotel rooms and only two-thirds as many slot machines as it did before Hurricane Katrina. A major bridge that connects the casinos in this popular tourist destination to Alabama, the Florida Panhandle and other points east remains closed, and Mayor A. J. Holloway estimates that as many as 15 percent of the city’s pre-Katrina residents still have not returned. Yet business in the gambling halls of Biloxi has reached all-time highs in recent months, so much so...