What was done
The authors compiled a comprehensive dataset of bird species richness in China - based on pertinent scientific literature published over the last three decades - for 207 localities (the vast majority of which were national nature reserves with a mean area of 3270 km²), which they then analyzed for their relationships to 13 different environmental variables.

What was learned
Qian et al. report that "of all environmental variables examined, normalized difference vegetation index [NDVI], a measure of plant productivity, is the best variable to explain the variance in breeding bird richness." More specifically, they determined that four of the 13 variables they tested explained 45.3% of the total species richness variance, with 21.2% being accounted for by NDVI, 12.5% by elevation range, and 11.6% by annual potential evapotranspiration and mean annual temperature together. In addition, they note that the two most important predictors of their study (NDVI and elevation range) "have been found to be major predictors for breeding bird richness in other regions and the whole of the globe [italics added], indicating that the finding of [their] study at a smaller scale is to a large degree consistent with those of previous studies of breeding birds at larger scales."

What it means
These findings make a lot of sense, for in a major review of plant-animal interactions in 51 terrestrial ecosystems conducted twenty years earlier, McNaughton et al. (1989) found that the biomass of plant-eating animals is a strongly-increasing function of aboveground primary production, while in a subsequent review of 22 aquatic ecosystems, Cyr and Pace (1993) found that the herbivore biomass of watery habitats also increases in response to increases in vegetative productivity. Hence, it should be abundantly clear that greater plant productivity - both terrestrial and aquatic - leads to greater populations of plants and the animals that feed upon them, which should therefore lead to greater ecosystem biodiversity, because each species of plant and animal must maintain a certain "critical biomass" to sustain its unique identity and insure its long-term viability. And that's where atmospheric CO2 enrichment enters the picture: it enhances plant productivity, which supports more animal life, which leads to greater animal biodiversity, which is good for the planet and good for mankind, who are the stewards of all life upon it.

References
Cyr, H. and Pace, M.L. 1993. Magnitude and patterns of herbivory in aquatic and terrestrial ecosystems. Nature 361: 148-150.

McNaughton, S.J., Oesterheld, M., Frank, D.A. and Williams, K.J. 1989. Ecosystem-level patterns of primary productivity and herbivory in terrestrial habitats. Nature 341: 142-144.