It would be helpful if you could link to the article.
High level answer without seeing the article would be the Upanishads for India, and the Book of Songs for China.
In terms of the Mesopotamian material, that is very old indeed, but difficult to link directly to existing cultures. Nevertheless, the Gilgamesh is believed to be the earliest surviving work of literature and the first epic.
It is worth noting that in the Chinese tradition, mythology and history are conflated until the 20th century, so much of the mythology comes out of histories by authors like Sima Qian and Chen Shou.
The Chinese tradition is quite distinct in that the gods are relatively minor in the literary canon, which tends to be focused on sages and the conduct. Figures such as Lao Tzu are mythologized and become gods. The Book of Songs is said to have been compiled by Ji Dan, the sage credited with the concept of the Mandate of Heaven, and subsequently deified. Lord Guan is elevated not for his military prowess so much as his impeccable conduct that made him a figure of veneration. Xuande, whose restoration of the Han is the subject of the Romance of the Three Kingdoms, can be said to be the the central figure in Chinese mythology, again, esteemed for his impeccable conduct. (Compare to Lü Bu who, despite his legendary martial prowess, dies an ignominious death.) In the warrior epic Water Margin, the central figure is Timely Rain (about the best epithet one could have in the agricultural society of China, where rain is the domain of dragons, and the name can be understood as the greatest of good fortunes). Timely Rain is the weakest fighters among the Outlaws of the Marsh, but becomes the leader because the heroes all venerate his conduct and sagacity. He fights with a jian, but is also a scholar. (Jin Yong titled one of his Wuxia novels The Book and the Sword, which can be taken as a metaphor for the Chinese tradition.) Huangdi, the Yellow Emperor, is a scholar and a sage, credited with innovation such as the calendar and mathematics. Similarly, his grandson, Emperor Yu, who developed a system of flood control, regarded as the single most important factor in the development of Chinese civilization, which is continuous over 3000 years. In this sense, the Book of Songs leads to a mythological tradition that is quite distinct.
For the Indian material, you may find the religious texts difficult to get through, due to the repetitions, but William Buck has excellent translations of the Vālmīki Ramayana and Mahabarata specifically adapted for Westerners interested in the stories.
On element that distinguishes Hindu mythology is that the Hinduism is still the dominant religion in the culture. This is distinct in the West, where Christianity supplanted the earlier, polytheistic traditions.