Your "most logical analogy" still isn't quite right. The individual scores for each game were very close, and the total scores actually slightly favor Clinton. But Trump won more games, after weighting the games in a certain way. But I don't know how to do it better, I don't think there's any sport that's really played anything like this!
I'd say the best measure for closeness would be either how much of a shift in the overall vote was needed to flip the result, or how much of a targeted shift could generate a change in the result. In this case, an overall shift of 1-2% would have changed the result, and a targeted shift of some tens of thousands of votes could have. It's not the closest election ever (2000 probably takes that prize by these criteria) but it's fairly close compared to, say, 2012 and 2008.
On further reflection, I do agree that the election was close. I'm guessing my previous response was conditioned on Trump being the underdog, arguing on a different point you were making.