I would argue that this case does not really shape the interpretation of the whole Constitution -- it is not about original intent or a "living Constitution" or any other issue like that which is fundamental to all constitutional cases. Instead, I would argue that this case was important in setting out limits on the idea of presidential immunity.
In the case, Pres. Clinton argued that, as president, he should immune from lawsuits against him. This immunity would end after his presidency, but while he was in office, it would exist. The Supreme Court rejected this reasoning, arguing that a president could only be immune from being sued over acts that were related to his duties as president.
By ruling in this way, the Court set a limit on the extent of the privileges of the president. For that reason, the case is important in terms of the interpretation of presidential powers.