It's "Second Game" by Katherine MacLean and Charles V. De Vet, referencing the spy who is found out because he's very smart and consistently beats people in their local strategy game (which is complex enough it makes chess look simple).
He plays each opponent, letting them win. Then, in the second game, he beats them. In this manner, he beats two of the world's best players (unknowingly) - this is a big thing, because the alien race chooses leadership based in part on playing ability.
The leader (the only one to beat him in the second game, IIRC) later comments to the spy that he has, indeed, beaten the species in 'the second game' - by diluting the alien species genes as you mentioned.
It's a short story I've seen in at least two compilations, but I can't find the author at the moment.
I emailed the fine folks at MIT's SF library (email@example.com) and this is the response I got (describing the work pretty much as I did above):
The story you described could be either the original novelette, "Second Game" by Charles V. De Vet and Katherine MacLean, which appeared in the March 1958 issue of 'Astounding' magazine, or one of the expansions. The first expansion was entitled "Cosmic Checkmate" and follows a similar storyline but is about twice the length of the original. I don't know when it originally came out, but there is a Kindle edition (ebook version) which is available for less than five bucks.
The second expansion came out in 1981, and was retitled to "Second Game," presumably to match the original more closely. It has a romantic subplot, which given your description makes me think that you read one of the first two stories rather than the third one.
The book review at http://www.sff.net/people/richard.horton/aced14.htm has more information.
Hope this helps.
Sincerely, - Susan Shepherd
This is a quote from a different question, which seems fairly similar.