The labyrinth in the story is a manifestation time itself, and of the attempt to circumvent cause and effect by choosing a lateral rather than linear narrative.
For Dr. Yu Tsun, time is running out, he knows that it is not a matter of whether he will be captured, but when. Time shows up here in its finite form, but Borges lets Tsun escape it momentarily when he gets lost in his thoughts of labyrinths: "I thought of a labyrinth of labyrinths, of one sinuous spreading labyrinth that would encompass the past and the future and in some way involve the stars. Absorbed in these illusory images, I forgot my destiny of one pursued. I felt myself to be, for an unknown period of time, an abstract perceiver of the world". Time becomes lateral here, Tsun exists in two different times.
But the true significance of the labyrinth motif in this story is revealed when Albert announces his conclusion that Ts'ui Pen's book is also the labyrinth he had set out to create. Pen had taken characters and events and had seen the possibilities of various choices of each event and followed each and every possibility to its end, omitting none.