What exactly are ‘new economy plays’ in the following sentence?
While new economy plays such as BYD may well turn out to be the future of China’s car industry, even they will not be exempt from the more sobering maths facing the country’s consumers these days.
A “play” here means an investment tactic. It can mean investing in a particular company, or a particular industry, or even using a specific tactic - maybe buy in December and sell in February each year. In your example it means to invest in “new economy” companies, though I’m not sure how that would be defined exactly 
Here is a website that uses it in the sentence:
In an arbitrage play, you buy something from one exchange or venue and sell it to another for a profit based on differences in the market price.
I would suggest the word ‘ploys’ as a meaning for ‘plays’.