The main way in which this scandal demonstrated the vitality of a democratic society was in the fact that the US political system continued to function throughout the scandal. Everything was done in a constitutional way instead of by force.
In a society with different habits, Watergate might well have led to the fall of the system. At the very least, it might have led to some sort of extralegal (not according to law) taking of power from Nixon. Instead, oppositional public opinion built to the point that Nixon decided that he had to leave office. The presidency was then filled according to the constitutional procedure for replacing a president. In this way, Nixon was removed and replaced in democratic ways rather than by force.
The fact that the US made it through the scandal without a major crisis and without any extralegal actions by anyone but Nixon and his staff shows the vitality of democratic society.