couldn't "vencer" be used as well here?
Vencer we often use to "win"
Can't it be amiga?
Yes, but you also need to change the possessive: "sua amiga". If that wasn't accepted, please report the whole sentence as being correct the next time you run into it again.
Why was is not amigo?
"Amigo" is a correct answer. Maybe you made an error in the sentence around it :)
Why was "o seu amigo" wrong?
It's also right.
Not amigo dele?