This thin line is known as the Hexi Corridor, located in modern-day Gansu province. The reasons for its shape are mainly geographical.

Encyclopedia Britannica explains this succinctly:

China’s physical relief has dictated its development in many respects. The civilization of Han Chinese originated in the southern part of the Loess Plateau, and from there it extended outward until it encountered the combined barriers of relief and climate. The long, protruding corridor, commonly known as the Gansu, or Hexi, Corridor, illustrates this fact. South of the corridor is the Plateau of Tibet, which was too high and too cold for the Chinese to gain a foothold. North of the corridor is the Gobi Desert, which also formed a barrier. Consequently, Chinese civilization was forced to spread along the corridor, where melting snow and ice in the Qilian Mountains provided water for oasis farming. The westward extremities of the corridor became the meeting place of the ancient East and West.

In addition to geographical concerns, there were foreign peoples already inhabiting those regions in the Gobi Desert and the Tibetan Highlands, such as the Uyghurs and the Tibetans, respectively. Obviously, they didn't take kindly to the Chinese freely encroaching upon their land, so if the Chinese wanted to expand west, the Hexi Corridor was the path of least resistance.