McCain did. As did Romney. But neither one pursued it.
You are exactly right. The candidates who received electoral votes and who had a chance to be elected but were denied that opportunity due to an ineligible candidate would be able to show direct injury from Obama’s election, and so would the political party that nominated them.
So McCain, Palin, Romney, Ryan and the Republican National Committee on their candidates’ behalf would have standing to bring suit or to enter an existing suit as lead co-plaintiffs.
None of the above chose to file a lawsuit or to join a class action suit.