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.)
There is absolutely nothing stopping an American, Japanese, Iraqi, Venezuelan, Russian, Chinese, German, or Indonesian company in offering its products for sale to foreign customers in Canadian dollars, yen, renminbi, dinars, rubles, Euros, or bhats. A US carrier isn't going to appear off the shores of your country for doing so.
They don't do so (or, when they do so, they also denominate in US dollars) because customers by and large prefer using US dollars. They also like using Euros, yen, and Swiss francs. (They have no problem with Canadian or Australian dollars, but obtaining it can sometimes be more difficult.) But the US dollar is the one currency that is absolutely, positively, 100% guaranteed to be wanted by both the buyer and seller, no matter where and for what.
Let me repeat: The primacy of the US dollar is driven by demand, not supply.
Also, these days it's less the petrodollar and more the technodollar as shown by the handwringing over US/China technological dependence/independence and how many key technologies in electronics/aerospace/biotech each country has or can develop to create a globally competitive and resilient ecosystem of technology products.
