South Asia had a completely different set of circumstances in comparison to the Islamic world or China and obviously Europe. For one thing, while the Delhi Sultanate was in a declining situation during the 14th century, economically there was little to no stress in South Asia and in some cases, South Asia was experiencing a renaissance in growth due to importation of an even greater number of Persianate scholars, merchants and general talent which began to migrate to South Asia to grant their expertise due to the fallout of the Ilkhanate in Iran.
I don't really agree with this part, south Asia began to ruralize from the 8th century and continue to do so steadily till the establishment of the first turkic dynasty in India after which expansion of rural network actually increased very rapidly and was undone only during the reign of Akbar, Shah Jahan, jahangir and aurangzeb when south Asia began to urbanize rapidly on the back of relative stability in the north brought about by the Mughal Empire and in the south by vijayanagar and the bahamani sultans and expanded trade network with Europe, Africa, middle East and China.
The migration of nobility from central Asia made things worse, be it may following the collapse of khwarazmian empire or the illkhanate, cause you had a large number of educated elite trying to sustain themselves off a very small economic base and which was even reducing, these elite weren't like the migrants who went to the Americas, these were nobles who after entering south Asia engaged in conflicts with each other and the native population, the Khilji's were in the service of the khwarazmian Shah, the tughlak too were off central Asian stock. I see the migration of these nobles who had very little knowledge of agriculture in south Asia or its industry or its governance as being of use , infact they were cause of general anarchy of the Era, ofcourse you'll find exception to the rule, prominent being Mughals, but you know those exception just prove the rule that these noble migrants were generally a rent seeking elites who contributed to the political instability if they didn't have things their way
The Pashto-Turkic sultanates were terrible administratively when compared to their hindu Buddhist predecessor or muslim successor Mughals or their Sunni brethren the bahamani who actually introduced perso Islamic culture to the wider population. Most of the public buildings constructed under the muslim dynasties here was under the Mughals or under the bahamani sultanate, the turkic sultanate just established a series of forts which was later taken over by the Mughals, the only monument worth remembering under these turkic sultanate was qutub minar and a handful of others, you just don't see the level of achievement of say their near peers the bahamani who too were terrible administratively but used the taxes to establish public buildings instead of just fort complexes and who actually imported Persian bureaucrats and experts and who did raise the standard of living marginally of ordinary people, for example you see a lot of qanats in the Deccan that supported large urban population in the north you see nothing of the sort, forget qanats which wasn't suited for the geology of the north, but they didn't maintain the irrigation canals or established new ones or maintain roads or caravansaries.
The turkic sultanates were basically what Germans would say is raiding/plundering economy of the Nazi German Reich , they imposed huge taxes on the people which made cultivation unsustainable and those taxes were collected irregularly and it wasn't unusual for the sultans to force people back to cultivation and one or two bad harvests you had famines, and to sustain the bloated and inefficient state bureaucracy they raided neighbouring kingdoms which made them poor too. What you see is a 300 years of economic mismanagement which caused a massive famines, mass ruralization, economic collapse in the north because of ill advised economic policy so much so even by the time of alaudin khilji you needed a total war economy too hold the state together which after him fell apart, you don't find a adminstration of his calibre in Delhi after him, what you had was a 200 years of war lord period, central control was weak and Mohammad bin tughlak threw into the fire what little legitimacy the state had, infact the bahamanis had enough of mal administration that the Persian nobles started to establish a independent sultanate down south.
So if the bubonic plague hits south Asia it would kill slightly less number of people because the rural hinterland has expanded so much that there's no concentration of people like in Europe or the middle East.
