People and countries outside the US don't use the dollar because of the US military, any more than they use the Swiss franc because of the Swiss military. They use both currencies (and the UK pound, and the Euro, and the Japanese yen) because decades of experience show that the countries that issue said currencies are the least likely to default on their financial obligations, and are most transparent about their own financials.

Russians and Chinese themselves avoid using their own countries' currencies when abroad as much as possible because they are most aware of this. To put another way, the primacy of the dollar isn't a supply issue (something that the US directly forces), but a demand issue (it's the currency everyone else prefers to use).

(This is where you'll bring up the "petrodollar". No, the petrodollar isn't real. Well, it's real in the sense that oil is, like almost every other product, usually denominated in US dollars when sold internationally. What's not real is the theory that the US has a particular need for (say) Iraq back in the day to denominate its oil sales in dollars, as opposed to Euro. Or that Venezuela attempting to denominate its oil in yuan today surely augurs the collapse of the US economy tomorrow.)