I tend to think the number is closer to $400 billion US when you weigh all conversions....
There are two distinct things you're trying to count here.
One is the economic burden of military spending. For that, any kind of conversion is meaningless. All that matters is 1) the local currency cost, related to the size of the economy, & 2) the hard currency cost, related to hard currency earnings. Any attempt to estimate a PPP figure as a share of the economy subtracts significance from this type of estimate, rather than adding it.
The other thing is the value of military spending, for international comparison. In this case, calculating a military PPP - or better, PPPs for the different constituents of military spending - is meaningful, & potentially valuable.
From reading John Tkaciks articles, it's clear that what he's done to get his figure is mix up the two aims. It's a "burden to the economy" estimate converted at an (inappropriate) whole-economy PPP. He uses an estimate of real Chinese military spending as 4.5% of GDP
in local currency, & total GDP at $10000 billion
at PPP (from the CIA). Does that make military spending at PPP $450 billion? Errr no - probably not, because the PPP for that spending is very unlikely indeed to be the same as for the whole economy. Military spending is probably much more capital-intensive than the whole economy, with a considerable hard-currency component. One of the rules here is that anything which is traded internationally should be priced at the international price for a PPP conversion. The PPP for military spending is probably much closer to the exchange rate than the PPP for the whole economy.
The methodology is grossly flawed. You
must use sectoral PPPs for sectoral comparisons! The articles are polemics, not analyses.
BTW, I believe the SIPRI figure of $140 billion in 2003 is an attempt at a true (i.e. sectoral) PPP estimate.