"Do the needful" is British bureaucratic English from the days of the Raj. It is not strange that various parts of the Raj have retained different mannerisms.
The linked article is extremely condescending and smug, (agreed, written by an Indian), and I remember reading it a while back. You might as well complain that Indians use the word "flat" instead of "Apartment" and use "colour" and "centre". By the way, two specific points against the article are merely literal translations of equivalent expressions in Indian languages, similar phrases will exist with other people for whom English is a second language:
1) "Do one thing" is a literal translation of "ek kaam karo", which is a valid Hindi expression. The ideal English idiom in the same spirit as the Hindi one would be "Try this:", which is perfectly reasonable.
2) "Sleep is coming" is a literal translation of "neend aa rahi hai", again which is valid Hindi.
One usage which is common to Indians, and cause confusion to even other Indians: does a student of a course "take an exam" or "give an exam"? What about the instructor of the course?
While on the subject, one could complain about silly Americanisms as well:
1) "We will be with you momentarily" - even if it is technically right this is slightly confusing: why not be with me for somewhat longer, dear? - "We will be with you in a moment" is unambiguous.
2) "Water with no ice" waiters/waitresses in the midwest stare blankly if you say "water without ice"
3) "To go?" - just step back and think what this means. It certainly does not immediately suggest a parcel.
and probably others. The point is: be thankful that English has the global appeal it has, and enjoy the quaint idioms of the different parts of the world which formed the British colonies.