They are having a sale [color=red]down at the supermarket.====> What does [color=red]down mean here? Is it necessary that a specific direction is implied here?


Not a specific direction, no. It might just as easily be ‘they are having a sale up/over at the supermarket’.
The ‘down’ is unnecessary (and makes the sentence sound like informal American English to me).

Just like the problem with ‘down the road/street’ and ‘up the road/street’, if there is no obvious hill or starting point, everything can depend on how you perceive where you are compared to that of the landmark.