Then explain the thousands of different dialects still being spoken in China, if you think that the Qin emperor decides to kill off all of his opponents? The fact is, he was brutal, and there were mass murders but no less than any other civilization at the time (Romans, etc). And to say he simply wipe out the other 6 countries' population is ludicrous. If that were the case, then there is no one in CHina that would speak anything other than Putonghua, and there isn't, there are thousands of dialects.
English has become a common language only over the last 500 years ~ before that, it wasn't even used in civilized society in its own country, and a thousand years ago, it was actually a totally different language more akin to Dutch and Danish than to what it has become.
The Period of Warring States was more than 2,000 years ago. That's plenty of time for new variations on an existing language to rise up in China. In fact, it's plenty of time for Latin to give rise to French, Protuguese, Gallo, Italian, Rumanian, Spanish and several other languages.