Translation:I am going to love someone who loves me.
It certainly can be, but "that" is also acceptable and widely used.
"In fact, people have been using that for human and non-human references since at least the 11th century, and that is handy if you want to talk about both a person and a thing." (http://blog.oxforddictionaries.com/2012/09/that-who-which/)
Why does the hint translate:
alguém = someone, somebody, anyone
if "anyone" is ONLY "qualquer um"?
I think it is wrong, yes. "alguém que me ame" is a relative construction, "somebody that loves me", and is the direct object of "amar". Who am I going to love? Somebody that loves me.
For your meaning (or for "I would love it if somebody loved me"), I think that in Portuguese you'd need to say something which literally means "I would love that somebody loved me" - "Eu adoraria que alguém me amasse".