The Esquire was a cocktail lounge on South 2nd Street right off Fremont Street. Listings and ads I have found run from as early as 1944 through the 1960’s. In 1944 the proprietor is listed as E. A. Robinson and then by 1949 on it was Walt South and Tommy Tobin.
The Esquire Bar had a gaming license issued Jan 23, 1948 to E. H. Brandhorst, L. Schivo?, and Walter South and another license listed as Esquire Club Games on Dec 1, 1951 to William L. Eakins. No types of games were listed or closing dates for the licenses. {from Fuller Index Plus}
The address 120 S. 2nd is now Casino Center Blvd and has been incorporated into the ever expanding Golden Nugget.