How can one deal with a young man who claims his relationship with a girl is "love for the sake of Allah" and justifies not leaving her by his fear of falling into sin if he does, while promising to marry her?

You must refrain from speaking to this young man, and it is not permissible to persist in it with false pretexts such as "love for the sake of Allah" or "fear of him falling into sin," for these are satanic pretexts. These conversations are a gateway to temptation and corruption. If he is sincere in his intention to marry, then let him propose to you and approach houses through their doors.