The Boxer rebellion is going to be crushed, the only question is how many lives (mostly Chinese, but also Japanese, British and Russians) is is going to cost.
The Eight Nation Alliance force that put down the rebellion is a pittance compared to what those nations could have committed if the rebellion had lasted even a few months longer. Russia, Great Britain and Japan could have assembled three or four times the number of men they sent IOTL in short order, and would not have been shy about committing those forces if they thought they were necessary. The rest of the Alliance (except for AH) would followed as best they could.
The Beiyang Army and its excuse for a navy would have been crushed in short order, no matter what they did. The local and provincial armies were not capable of united action at this time, they may or may not have opposed the ENA when they encountered it. The ENA warships would have cruised all of China's navigable rivers, transporting troops, and devastating any cities/forts that resisted.
If enough damage is done to the Quing dynasty, it would not be impossible for the Allies to overthrow it entirely, like the British did to the Moghul Dynasty after the Sepoy Rebellion. With Cixi dead, and its armies defeated, and its capital and major cities in ruin, the Quing Dynasty would simply cease to exist. Of course, that would require the ENA to agree about splitting up the Chinese Empire into spheres, which would be a greater challenge than overthrowing the Empire militarily. However, the Congress of Berlin does suggest that they would have come up with some arrangement that would not have immediately led to war. Japan, at this time would probably gain the least, as Germany, France and Russia were at this time cordial enough to gang up on what they viewed a weak and unwelcome interloper.