That's the first thing I thought of too! Glad that I got beat to the punch.
Precisely... I don't get it either. (Linguist mode on) After all, the dropping of the relative marker (not sure whether relative pronoun or not) is common in English nowadays.
Because "die" means "that". You're expected to translate these word for word, so by saying "Am I the one you want" you are omitting a word that is in the sentence. It does make sense, but it's not what the sentence above says.
That would be Ben ik degene die jou wil?
Die je wilt - That you want
Die jou wil - That wants you
Why is it though? "Je" is the unstressed version of both the subject and the object pronouns. Is is that because you used the unstressed version in the first sentence, people will automatically understand that the word works as a subject?
It's a different verb form: jij wilt (with -t), hij/zij/het wil (no -t). Willen is irregular.
However, in this case: 'Am I the one WHOM you want?' Cf. Leonard Bernstein's Wonderful Town, 'One hundred ways to lose a man': http://www.metrolyrics.com/one-hundred-easy-ways-lyrics-wonderful-town.html or https://www.youtube.com/watch?v=uNDRmCsm3RQ
I don't understand why 'Diegene' was rejected. The previous sentence was 'Is hij diegene die van je houdt?' (Is he the one who loves you). Looking at the discussions it appears degene and diegene are interchangeable.
In many cases diegene (literally that one) does work, but together with Ben ik it doesn't, because the first person cannot be that.
If you use "je" would the sentence not translate to "Am I the one you want?", and if you use "jou" would it not translate to "Am I the one who wants you?".
Je is the short form of both jij and jou. Initially confusing but true. In this case the difference is in the verb form: jij wilt, hij (degene) wil.
You're right. It can be confusing. In "Am I the one that you want", it is "you" who is doing the wanting. In "Am I the one who wants you", it is "I" who is doing the wanting - i.e. "I want you" or "Ik wil jou", not "Ik wil jij". See also JustCallMeRemko's comments above.
My guess is "Ben ik degene die jou wil?", but a native speaker might correct that.