Would it be okay for me to ask out a girl who is non-exclusively dating my friend?
Are you sure your friend's girl will date you?
Yes I'm sure, she likes me a lot
Even though your friend and his girl are in an open relationship, you hooking up with her would still be wrong because she is still with your friend. Getting involved with your friend's girl will destroy your relationship with him.
So what, he's just one person.
That is your friend, it doesn't matter if he's just one person, he is supposed to be an important person to you. If you care about him then you won't attempt to swoop in and steal his girlfriend.