Kellinator Jones and the Temple of Snark

You were correct in your supposition of "Who". Who and Whom can be viewed as parallels of "he" and "him". When you can use he, use who, when you can use whom in its place, use whom. I was confused when I first started to try to figure out which was appropriate, because I think "they claim" should be set off by commas, but I'm not sure on that. All I know is that "who" is the subject of "should have won" which was interrupted by "they claim". See, you could say "He should have won" therefore you say "who, they claim, should have won". Yay for grammar! Watch me be wrong. ha!