You are absolutely right.

These establishments were known as "bungalow colonies".
The "hey-day" for these places were the post WWII years through the mid-1970's.

During the summer, many New York City families would stay at these places.
The wife and children would spend all summer there and the husbands would drive up (or take a bus) to stay the weekends.

Every bungalow colony had a social hall where everyone gathered in the evenings. Every bungalow colony called that social hall "The Casino".

You are not exactly correct about the gambling - there was plenty of gambling - poker, pinochle, canasta and mah-jonng were popular though the stakes were modest and the gambling was just between the participants. There were no "chips" that you bought - you just played for cash on the table.