I agree that the last stand and the underdog are both romantic visions that we enjoy, but I don't agree that it has anything to do with a selfish desire for martyrdom.
Games are about challenge and the personal reward of overcoming that challenge. What could be more challenging than being matched against impossible odds? Winning against the impossible is its own reward -- knowing that you did what few others could do. There's also the recognition from others that you managed it. And lastly, there's the enjoyment of seeing something out of the ordinary, different, unexpected. We love to see the impossible happen.
As for why we make our last stand, I think it has a lot to do with hope and pride. Hope that, as impossible as it seems, you might still have a chance (because sometimes all we have left is hope), and the pride to not want to fail, to not turn down a challenge.
I've been there before. I've played many a game of Counter-strike against a team whose record in the tournament was better than my team, but that didn't stop us from persevering. We wanted to win, and we knew that the only way to do that was to try. It didn't matter that the odds were against us and that we were likely outmatched -- we had hope that we could pull it together, or that they would make a mistake, or that some way we would be able to win. I remember a few rounds where it was me alone with a pistol vs. 4 guys with SMGs. Was I screwed? Hell yes, but I wasn't about to give up and give them an easy kill -- I still wanted to win. Part of it was just wanting to win, part of it was knowing that my friends were watching and hoping that I could do it. I knew there was the expectation that I at least try my best. I also knew that there would be great recognition if I managed to win. There were so many more reasons than just wanting to be remembered as a martyr, especially since I knew that my martyrdom wouldn't be remembered by anyone when the next round started.
Most of the time, I died, and I felt no failure for doing so. But every now and then, I won against all odds, and it was a truly satisfying victory.
We stand up against impossible odds because we have hope that the impossible can happen.