Possibly he was a little melancholy because he knows it was probably the last game his brother would be playing. It's the end of an era for them and their sibling rivalry. This also probably brings to his mind thoughts about his own longevity of time left within the sport. My guess is they've been playing football together since their early childhood. In any other occupation age 39 is not considered retirement age.
I think the idea that he's mad about Peyton tying him in ridiculous. These people are playing at a higher level, sure it's competitive but like Peyton said, they don't do that. My brothers & I don't/wouldn't either. It's childish. I believe Eli was analyzing the game from a QB perspective, & probably having a more "sigh of relief" moment, than a "yay my bro's gonna win" moment. He's been in that stressful situation, & he also knows that games aren't ever guaranteed until the final second ticks off.