The article to which you have linked is actually part of a book that deals with how people should behave in their online lives. The “dinner table rule” is a rule to help us understand what actions and behaviors are acceptable online.
The author in the link argues that the dinner table is the place where we act in the most civil possible way. When we are there, we are typically eating with people who are important to us. Therefore, we try to behave in proper and acceptable ways.
Therefore, the author proposes, we should think about the dinner table when we are deciding what to do and say online. We should ask whether the action or words we are considering would be acceptable at our dinner table. If we cannot say that they would be acceptable, we should not do them or say them.
Thus, the dinner table rule is a rule that the author proposes to govern our online behavior. It asks us to behave online as if we were at our own dinner table.