Ob das wirklich Jungs sind, die hier ihren Drachen steigen lassen oder vielleicht sogar verkleidete Mädchen?
Is ihren Drachen accusative singular or plural? I ran it through Google Translate and it says their kites, i.e., plural. But shouldn't plural be ihre Drachen? Adding an n to ihre to make it ihren looks to me like masculine accusative singular.
Source: https://www.kinderweltreise.de/kontinente/asien/afghanistan/alltag-kinder/kinder/
Your assumption is correct, and Google is wrong (sortof and maybe).
The possessive pronoun ihren is definitively accusative singular.
However (this is a bit off-topic, because it's more about English than about German): While German does not really care that many boys maybe use many kites (and can thus use the singular, even if it's most probably many kites), English is a bit more precise here and requires you use plural when each boy or girl has their own kite.
You could say there is no way to translate this sentence literally, assumed the kids do not share one single kite.
Astonishingly, Google is clever enough to get the pronoun right when you ask it to translate a sentence that makes it explicitly clear there is only one common kite:
Die Kinder ließen ihren einen Drachen steigen
translates to
the children let their kite fly
Die Schüler sollen ihr Englischbuch rausholen und die Seite 23 lesen.
is a perfectly acceptable German sentence, and every pupil will assume to read their own book.
Pupils are asked to open their textbook and read page 23
Would be considered wrong (or rather, irritating) in English because pupils are assumed to each have a book of their own.
As you suspected, "ihren Drachen" means many owners of a single kite, I think you got that perfectly right.
The original German sentence implies that kids (plural) fly their kite (singular). The interpretation "of many kids each flies their own kite" isn't totally wrong, but strictly spoken it is not what's written there. One kite/many pilots is just improbable because usually everyone, boy or girl, flies their own kite. It adds to the fun, I can tell.
I am not into google's algorithms and can't say why it translated that sentence, arbitrarily converting singular to plural. In this case this probably wasn't totally devious, but in another context it may change the meaning and may simply be wrong.
