To answer this question, we must look at both Chapter 12 and Chapter 6 of the Brief Second Edition of Traditions & Encounters. The earlier chapter discusses the Qin while the later chapter discusses the Sui. The answer to the question can be summed up in two very similar sentences. First, from p. 109:
Qin rule survived for only a few years, but the succeeding Han dynasty followed the Qin example by governing China through a centralized imperial administration.
Second, from p. 224:
Yang Jians’s Sui dynasty survived less than thirty years, but the tradition of centralized rule outlived his house.
In short, Bentley and Ziegler are saying that both of these dynasties influenced China by giving it the idea of centralized government.
The Qin dynasty was the first to unify China. However, it held power for only 14 years. While it only held power for a short time, it gave rise to the Han dynasty, which ruled for more than 400 years. By creating a centralized government, the Qin set an example that would be emulated by the Han.
After the Han fell, no one was able to take control over all of China until the Sui. The Sui were able to conquer all of China, but their dynasty only lasted about thirty years. Like the Qin, though, they gave rise to other dynasties. After the Sui, the Tang ruled for almost three hundred years. After them, the Song ruled for a similar period of time.
Both of these dynasties, then, influenced Chinese history by setting examples. They both inspired other dynasties to arise and to continue to rule China as a unified country.