When failing a state, the systempunkt is the target which inconveniences the largest number of people through the reduction of critical services. When coercing a foreign state, the systempunkt is the target which has the greatest impact on that state's connections to global markets. In some cases, they are one in the same.
NOTE: I've been asked by a company to provide insight into a model of next generation warfare that the US security establishment can wargame against. To get my head in the game, I am channeling (in my meager way) Sun Tzu.