Before I answer, I must note that 'existentialism' itself as a concept cannot, as you have attempted, be defined completely context-free. As such, any sort of 'existentialism' in the continental European framework simply cannot be applied to China's historical context. European existentialism is derived from European nihilism, which in itself is a contextually derived historical occurrence.

Putting that aside, elements of existentialism (in its broadest sense) does indeed appear in Chinese intellectual thought. Ming dynasty scholar Wang Yangming's philosophy of mind believed that it is not the world that shapes the mind, but the mind that gives reason to the world. Therefore, the mind alone is the source of all reason. Where this differs from your definition of existentialism is that he understood this to be an inner light, an innate moral goodness and understanding of what is good. The cultural implications of this is that such developments in Confucianist thought added to the already complex strands of Confucianism, and added more individualistic elements to Chinese philosophy.

The article Moral Decision in Wang Yang-ming: The Problem of Chinese "Existentialism" by David S. Nivison in the journal Philosophy East and West provides a much better contextual analysis of existentialism in dynastic Chinese thought.