Not based on the semantic domain of the phrase. "Strong drink" is usually referring to alcoholic - though not distilled - drinks.
There were no distilled drinks back then. So what would a "strong drink" be? Did they have other alcoholic drinks other than wine and beer? Wine is a stronger drink than beer, so check your history and then tell me what "strong drink" is.
I suggest it is probably some kind of fruit wine made with added sugars (kinda like brandy). It certainly wasn't anything like tequila, or gin or vodka.