The poet and his guest are clearly on some sort of prominence - a mountainside pavilion, probably - contemplating a long journey by the guest to the capital where he hopes for a favourable appointment. Having just completed a game of go, the poet tries to lighten the gloom of the first two lines by optimistically recalling the time when Yang Xuanbao was summoned to play with the Han Emperor Wu Di and came away well rewarded.
Yang was an official of the Song Dynasty in the era known as Northern and Southern Dynasties. He served the Emperor Wu Di, who reigned 420-423. He had what was originally a rather grand title, Gentleman Attendant of the Golden Horse Gate, though by his time he was little more than a supervising secretary. But he was known as a good go player, of the third class, and was summoned once by the Emperor to play for the stake of the governorship of a city. He won and so bounded up the career ladder. The incident is referred to in another poem by Wen Tingyun, and must have been regarded with at least a tinge of envy.
The Golden Horse Gate itself refers to the Palace. The even more glorious Han Emperor Wu Di (the Song Emperor was of the same house of Liu) obtained a horse from Ferghana, modern Khokand, which was famous for breeding the finest animals. He ordered a bronze of the horse to be cast outside the Lu Ban gate (Lu Ban being a man from Lu later deified as the god of carpenters) which thus became known as the Gate of the Golden Horse, later abbreviated to Golden Gate.
The other place referred to is Jiangdong, an old alternative name for Xuancheng, an area around the southern bank of the Yangzi, below Wuhu, near Nanjing. It was this city that Yang won.
Farewells are a very common theme of Oriental poems. The slanting flights of autumn geese departing for their long migration south obviously refer to a farewell but I have assumed they also hint at the shapes made by go stones in a running fight.
A small technical note: shiqi here is an inversion of qishi, because the 6th character of the line must be an oblique tone.