The other answers have pretty much said it all. If none of those work, you could try mimicking her behavior: let her win at a game sometime, pretend to bawl your eyes out, and the game ends. Ask her how she feels when the game ends just because you lost.
I know it sounds a bit crazy, but when dealing with such behaviors, we never know what will work.
If you do try this, I would suggest "surprise" her. Don't tell her "we are going to see what happens when I cry at losing". during a regular game or play time, behave like her, and see if she gets it.
And, kids behave totally different with us than with their friends and peers. My 5 year old has to always be the first at everything at home, and throws a big tantrum if not, but at school, he has no problems lining up, taking turns, in the classroom and also in the playground where there is no supervision. So, maybe your kid, given that she is ahead in most things, will figure out for herself that she has to be a sportive loser at times to make and keep friends.