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USA v Niue at rugby sevens
319 million versus 1.2 thousand (266,000:1)
Russia v Alderney at cricket
140 million versus 2 thousand - (70,000:1)
I can't find any others that come close to this.
China v Guam in football/rugby union is only around 8,000:1 in terms of population ratios, but has a much larger population difference (over 1.3 billion).
In terms of population ratio, if China/India has played a team with a population smaller than 5,000 in any sport, this would beat USA-Niue in rugby sevens.