Since nobody was living there (the only structure was an old fort), I believe it belonged to no one. Hence, the land was unused and deserted. China only used it for convenience (and by my standards, putting a road, to help save travelling people's time, isn't 'claiming' the land). Furthermore, India could also have used it (maybe also to build roads for convenience?)

The right of claim over the disputed territory of Aksai Chin was neither India or China. However, India should not have reacted harshly and critically towards China building a highway across Aksai Chin (which was for convenience of travelling to and fro Tibet and Sinkang). This resulted in a war which was inconvenient for both sides (who would want to fight in a war?). Furthermore, India could have also shared the land if both parties were willing to cooperate.

War is a negotiating approach, but not a goal. Similarly, China's decision to fight back against India in the 1962 border war was to strike a peace with its neighbor. Therefore, while fighting with the Indian troops, China constantly urged the Indian government to end the conflicts and solve the border issue on the negotiating table.

China initially tried to avoid military confrontation, out of respect to India's ancient culture and sympathy that it had suffered a similar painful past of oppression by colonial powers. However, India's persistent provocation eventually breached China's bottom-line, and the People's Liberation Army (PLA) was forced to join the battle in self-defense