Internet gambling has helped to give Atlantic City casinos a boost in revenue last month. In June, an increase of more than 23 percent in online winnings gave the city’s seven casinos a total monthly increase of 1.8 percent compared to this time last year. The Golden Nugget had the highest percentage increase of nearly 23 percent, bringing in more than $23 million. Caesars was the only casino in the city to report a decrease in June — of 1.9 percent.