Mongols that live in China are Chinese, absolutely.
And there are by far more Mongols in China than there are in Mongolia. We have more than double the number of Mongols that Mongolia itself has, and all the most fertile areas of Mongolia.
The Manchus and the Mongols of China willingly assimilated into the Chinese identity, they speak Chinese and follow Chinese culture, they have become Chinese people.
Maybe they were not considered Chinese before, but neither were my own ancestors (Hakka origin). The Huaxia were originally one tribe along the Yellow River, and like all other identities they assimilated others and expanded.
Same with the Anglo-Saxons, or any other group. They were once one small tribe, now they control massive swathes of the Earth's landmass.
Some tribes succeed, most tribes die out. A thousand years ago there were thousands of different tribes and religions dominating the world, now only a few dominate. This is how the world works.