First, there is no such thing as the Chinese language: Chinese is a language family, and there are far fewer people who are fluent in the politically dominant member, Mandarin, than the Chinese authorities would like you to think. Second, the Chinese languages share a writing system that is simply not fit for purpose: taking years to learn, and incredibly hard to adapt to many purposes, it is holding China's progress back by many decades. And third, nowhere in the world is there a country outside China where Chinese is used by non-Chinese to communicate with other non-Chinese.
Yeah, right. The existence of language varieties that are not mutually understandable (Scots, anyone?) and a crazy orthography sure have prevented the rise of English. Yes, it won't happen in the next fifty years, but Pullum's stance (although, of course, not his reasoning) looks a bit like that of an 18th century Frenchman regarding the possibility that the language of that rising merchant power from the neighbouring island would ever be able to challenge the dominance of French as the lingua franca of the civilised world. I doubt that orthography, writing systems, or the existence of non-standard varieties play any role in determining whether a language attains the status of lingua franca - it's all about the political, commcercial, and cultural influence of its speakers. It's fairly well possible that China will never reach the degree of political, commercial, and cultural influence that today's English-speaking nations (first and foremost the U.S.) have, but that (and not the writing system or whether Putonghua can crowd out the other Sinitic languages) will determine the status of Chinese in the future.