I don't doubt that the story was originally written with a gay relationship in mind. The ancient Greeks and then Romans did not have our much later Church-installed misnomer views of love and relationships.

There was no such thing in the Greek milieu as homo- or hetero- with regard to sex. There was just sex. Sex was never delineated by what gender it was with until the Roman Church began to install those delineations.

The Greeks had many different terms for love as well: eros, ludus, pragma, and what most of us have heard, agape. Today, we just call it love, but we have lost better definitions because of the misguidance of the Church, sadly.