The German dialect it used was a colonial dialect that already contained mixed features from multiple dialect area and was thus suitable for a wide audience.
Of course the emerging standard underwent development since then, and low literacy rates meant that few people actually spoke and wrote it.
If you want to go this route, then you could also say that the origins of Standard Chinese date back hundreds of years, to the language spoken by the imperial bureaucracy, or to massively popular works written in vernacular Chinese, like the Dream of the Red Chamber (late 1700s). There are always ancient antecedents that you can trace, but they become less and less directly related to the development of the modern language.
Yes, the Luther Bible was an important influence on the development of a standard literary German, but if you want to trace the development of a standardized spoken dialect of German, you have to go to the 19th Century and the development of Bühnendeutsch ("stage German"), which because of its use in theater had to have a standard pronunciation.
Standard German is not that old. It was largely developed in the 19th Century, and it was not until the 20th Century that most people in Germany were able to speak it. Standard German is also heavily based on a regional dialect of German (in particular, central German dialects).
Standard Chinese is a product of the early-to-mid 20th Century, so about 50-100 years younger than Standard German. This just reflects the fact that German unification was in the mid-1800s, while China's modernization occurred in the early 20th Century.