While nominal GDP certainly has its problems as a means of comparing output, PPP GDP is not necessarily any better and in many cases is actually worse. The main reason for this is that the product mix of different countries at different development levels and different industrial compositions is, well, different. To compensate for this economists have to either make dramatic compromises on what constitutes the 'same product' or, more commonly, they simply leave out large swaths of countries' product mixes that they do not share with each other. This will obviously tend to be biased against richer countries since they make many things that only a handful of other countries are capable of making, and so much of their product mix will simply be left out of the PPP calculations, causing their GDP to be substantially understated. When using the PPP measure, then, you will get results like India's GDP being over double that of Japan or Germany's, or Russia's GDP being over 2.5x that of South Korea. So while nominal GDP does tend to overstate rich countries' output due to things like imputed rents and the effects of labor costs on exchange rates, PPP GDP tends to be just as bad, only in the opposite direction. China's economy relative to the US is certainly bigger than nominal measurements would suggest, but it is very likely that the PPP measure goes too far in compensating for this.
We do not know what is causing the decline in reinvested FDI earnings, and I can think of at least four plausible reasons why it might be happening, but have not yet seen convincing evidence for any of them. I would recommend against speculating much in any direction until we have more information.