I'm not aware that the Chinese ruled and wiped out "real" traditional Mongolian archery, unless you are referring to the Cultural revolution, in which the Communists repressed that kind of stuff nationwide. Its only recently that Chinese archery is under going a revival in the Mainland since much knowledge, craftsmanship, and continuity was lost. I also don't believe the Communists ever get to rule and instill that kind of tyranny in Mongolia.
If you are referring to the Qing dynasty under the Manchus, I'll refer you to my friend Peter Dekker's article.
http://www.manchuarchery.org/did-qing-ban-archery-mongolia
Mongolians had much influence and status in the Qing dynasty. It doesn't make sense to disarm military elite people who are going to fight for you.