I never understood this mentality. I am genuinely happy when I see someone on, say, "Who wants to be a millionaire" win big. It's exciting! Why would I begrudge that?
On the other hand, I'm one of these braggarts who don't realize they (apparently) upset others so maybe I'm just weird.
I feel similar to you. Even if someone else is blatantly bragging, it has nothing to do with me.
If i feel annoyed, it's either i have some weakness in my psyche or that person is standing in my way. If it's my weakness, i try to fix it via introspection. If the person is trying to mess with me, i'll go for the conflict.
If I win the lottery, and I tell people, that's not really bragging. It doesn't really mean I'm great or better than others, just that I had good fortune.
On the other hand, I'm one of these braggarts who don't realize they (apparently) upset others so maybe I'm just weird.