Moreover, why was it so seemingly dysfunctional? It's goal was to maintain world peace, but it obviously failed in that regard (WWII and the events leading up to it.)
Furthermore, are current multi-national organizations doomed to failure as well? Is it feasible to say that the UN is likely to follow suit and fail in maintaining world peace? If not, how does the UN differ from the League to make it a stronger organization than the League?
The League of Nations failed in part because of its lack of ability to enforce laws. For example, when the Japanese attacked Manchuria, the League obviously told them to back off, and since they had no fear of military retaliation by the League, they simply left it. Another reason for its failure was that the United States did not actually join, even though they brought the idea up. This basically doomed the League of Nations from the start.
The USA didn't join it, but I'm sure you know that; so that brought down it's power and influence substantially. Also, no country was actually willing to take action against another, they kept compromising and compromising until it was too late. When the Japanese invaded Manchuria, they did nothing. Same with Italy and Africa and Germany with the Czechs.