This is surely some style guide thing, but I'll link and excerpt six Reuters headlines:
"Pakistan military rescues..."
"Pakistan crowd vandalizes..."
"Anger as French government..."
"German military in worse shape..."
It seems a tad unusual that some stories will use the Demonym form ("French", "German") and some will use just the noun name of the country ("Pakistan", "China"). I would have expected that Pakistani or Chinese were the more natural form to use in the headlines. I would find it hard to imagine seeing the "Germany military" or the "France crowd". After trying to research this I also found a recent NYT piece that says "China Central Bank" instead of the possessive "China's Central Bank" or "The Chinese Central Bank" or its actual name.
It does not appear to be 100% consistent in that "China's" and "Chinese" is used sometimes by Reuters, but it does seem like there is some kind of style norm guiding how to refer to each country's government. I would be open the idea that I am mistaken and this is just down to individual sentence construction and I'm seeing a pattern when there is none.
What is the underlying style rule that governs this? Answers can use any style guide, I chose my examples from Reuters but the question is broader.