Un this context, “a dig” means something like “an insult”.

A dig is kind of a gentle insult. You can make a dig when you're teasing someone you know well. If my friend is always late, I can say, "Dinner is at 6:00, so we'll expect you around 7:00." And my friend might say, "Is that a dig?" meaning, "So your point is to invite me and also to tell me that I'm late for everything?" Or, if someone says, "You look so young in that dress!" I might ask if that's a dig, thinking that the person is telling me that 1) I usually look old, or 2) the dress looks childish. A dig can be a passive aggressive way of insulting someone without having to look like a bad person yourself. I couldn't hear the audio in your clip well enough to know how friendly the two women are. But a dig could be a form of friendly teasing or a genuine insult in disguise. Context is everything. I hope that helps!