I don't know what standard there is for genuine Hindi literature but I happen to know a thing or two about Urdu literature. Everybody was able to interpret the text to their liking and what a richness has this aspect of Urdu poetry proven to be! Apparently it matters not what the poet wanted to say but what it does to the reader. It happens the text in the OP is Urdu poetry so let me continue. I can share a couple of points, taking a position on *all* what has been claimed would be too much and I don't think it is needed to clarify the problem.
The introduction of Ghazal tradition as a Persian and Urdu literary genre was necessary because it is the answer to why masculine is there. NOT because of claims to authors' sexuality.
Of course, 'they'/'them', are not new words in English. The BBC article you mentioned uses the term because the sex of the individual is unknown. That's different from modern gender theorists who insist they are neither male nor female, but some other gender(s), and thus eschew 's/he' for 'they'.
I was talking about the specific (singular) usage of "they/them" which is old in English, I wasn't arguing about the age of the word "they" itself, naturally.
The example from the BBC served as an illustration of a kind of usage unrelated to any ideology.
The reason for the masculine plural is exactly this: because the sex of the individual is unknown.
The poet's love-interest, "the beloved", doesn't inhabit the material world with its norms of language and gender, in the internal world of Ghazal, the figurehead of a beloved is a well-defined background prop which together with other regular characters of this literary kind provides the poet with expression possibilities.
Were it the wish of the poet to state the gender outright he would have no doubt known how to do it and I think that as far as the context doesn't give any definite clue to the love-interest's sex, we must not forcibly try to assign a gender to the beloved when the writer chose not to do so and simply accept the fact that the gender of the beloved is unstated thus irrelevant.
Not wanting to go to much off-topic,
[Edit: remove offensive comment]
The post remains aggressive.
To set the record straight

:
"Gender ideology" was introduced to the discussion by none other than yourself yet you continue to go that path in order to display intolerant views.
From "gender ideology" you managed to single-handedly glide onto homosexuality, so that you could out a historic religious group collectively with the Western 20th C. term "homosexuals".
This much about being on topic.
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Just to add to the thread:
The non-binary usage of "wuh"="they" is equally relevant and there is no need to exclude it arbitrarily just because of one's personal disapproval; it doesn't matter if you like it or not. The social phenomenon has strong and ancient rooting in South Asia. ''Third sex'' enjoys legal recognition in Pakistan, to take an example.
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The matter of
plural is liable to interpretation as well, because a lyrical subject is not bound to be a monogamist. This poem or similar can be very well understood to be speaking about a plural number, with or without the honorific aspect of the plural verbs.
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Amongst the people on the receiving end of the literary process are women.
Do you think a male poet would never write a piece in which a woman could recognise herself?
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Is it really so hard to imagine a male being the object of love by a male? Or a transgender?
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A woman? Sure! If respectable ladies can talk like old gentlemen (in Urdu) using the masculine endings?
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I have been reading the collected works by the above mentioned Shakeb Jalali and I've read the first half already looking for definite clues towards the beloved being feminine and I haven't met with any.
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I'm OK with mentioning Hindi when speaking of Urdu whenever linguistically relevant but since Shakeb Jalali did not write in Hindi... On the other hand it's depressing one can't use simply "Urdu" in a thread on a piece of Urdu poetry situated in the Urdu literary tradition without the obligate "Hindi".
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Qureshpor SaaHib is right pointing out the mindset which unnecessarily seeks sexualizing matters.
The film with its song had missed me, I regret I've had a listen. Made so banal and literal. (U) Poetry is not literal.
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ae miir, yaaroN se kaih do, kih aatii hae urduu zabaan aate aate