So, the Mughal Empire was founded by descendants of the Timurids, who ruled much of Central Asia.  It began in 1526 and went into decline after Aurangzeb died in 1707; it limped on, in name at least, till 1857, but for much of that time it was actually a British puppet state.

At its greatest (actual-historical) extent, around 1700, it covered most of what's now India, Pakistan, and Bangladesh, and some of what's now Afghanistan.  Map, from wikipedia:



In my alternate world, the Mughal Empire never stretches quite this far west (or nearly this far south); it did so in Aurangzeb's time because, frankly, he overextended pretty catastrophically, which is why the empire collapsed after he died.

Here's the Empire under Akbar (wikipedia again):



And here it is in 1650, which is the greatest extent it has in my alternate world. (In my world, Jahanara goes for stability over expansion.) From the WHKMLA historical atlas, which has a nice progression of the expansion & collapse of the empire:



Now, (some of) what we now call the Middle East was in fact considered a cultural center to the Mughals; obviously Mecca was the religious center, but Iran, especially, was the cultural center they both looked up to and chafed against (my interpretation). From Akbar's time onward, the official language of the Empire was Persian (though Urdu took over in actual usage), and there's a whole range of paintings whose rhetorical/political purpose is to demonstrate that the Mughals are JUST AS GOOD AS THOSE PERSIANS REALLY OR NO EVEN BETTER SO THEEEERE!

So, three things to take from this:

1) it's unsurprising that the setting might register as Middle Eastern, but really, no.
2) it's also not accurate to call it Indian, per se, except that - specifically - my story in the Mammoth book is set in a part of the Empire (near Agra) that's in India.
3) Never get involved in a land war in Asia.