No it doesn't. I don't subscribe to fidelty criticism.
There are plenty of stories which are totally different from their source material that are still considered adaptations. You don't need the same cast, same motivations or anything like that to not be considered an adaptation.
One of my favourite adaptations ever is Akira Kurosawa's Ran, which is adapting King Lear. Its a radically different from King Lear, but is still widely considered an adaptation. Hell, from my understanding, the director of Ran didn't even have King Lear in mind initially, it just sort of turned out that way.
So let me get this straight....
A story set in a different time period, in a different continent, in a different culture, with a different cast, with nobody even having the name Lear, with the creator supposedly not even setting out to create an adaptation in the first place and is at best only taking inspiration from a centuries old story...... Is somehow considered an adaptation?
That sounds completely bullshit.
Yeah, it can be a perfectly good film but an adaptation? Nah son, that is way too much of a stretch.
That would be like saying the Lion King is an adaptation of Hamlet. Lel.
Big difference between taking inspiration from something and making an adaptation.
If it's "radically different" from King Lear then it ain't King Lear.