The dollar isn't dominant in international trade because the domestic market is free, like the above user was referencing. The dollar has been the dominant reserve currency and currency for international trade since it overtook the pound for both of those functions in the mid 20th century, which didn't coincide with the US having a free market.
Also, I wasn't make any causal relationship in my comment, like you seem to be implying. The fact that USD is the dominant reserve currency and dominant trade currency is unquestionably more unique than having free markets, considering that the US is truly completely unique in both of these regards, while it is not nearly as unique in having a free market.