How did the boxer rebellion lead to the decline of dynastic rule in china

I would say that the Boxer Rebellion was simply the last in a long line of events that weakened China relative to the powers that occupied (but did not actually colonize) that country. The Boxer Rebellion did not really change the political structure in China in any great way. The Qing Dynasty did not fall, the Western countries did not actually take control of the country, but neither were they expelled. The Rebellion simply underlined the weakness of the Chinese government and gave the West and Japan more power over China.