The Legend of Zelda: The Breath of The Wild will be the first time alcohol has ever been directly referenced in the franchise. Recent ESRB ratings have the game listed at E 10+ for depictions of alcohol and moderate cleavage. The cleavage comes from the Great Fairies, who haven't been called out on their scandalous behavior since Ocarina Of Time and Majora's Mask. 

The drinking mentioned in the description was noted by an NPC character who is seen stumbling and hiccuping. That doesn't necessarily mean that Link himself cannot drink, but it was not directly mentioned in the ESRB so we have no idea one way or the other. You'd have to wonder if Nintendo would allow one of their characters to appear "drunk" given their family friendly nature.

Until now, the series closest reference to alcohol was seen in the "Milk Bar" in Majora's Mask, but it's also worth mentioning that Milk Bars exist in the real world as well. 

Even with the alcohol, the game still is rated for a younger audience than The Legend of Zelda: Twilight Princess. The game marked the first Teen rated title in the series for its more realistic type style of executions and darker themes. Do you think Link will have the ability to get drunk in this game?

Source: Polygon