It appears to be correct for volume and pace in terms of evacuating civilians from a hostile environment, but it also depends how you define "airlift."
Most of the historical references to big airlifts talk about weight of material moved, such Allied forces carrying 2.3 million tons of goods to Soviet-blocked Berlin in 1948-49. That's also cited as a record-setting personnel-moving airlift because the planes involved ferried 227,655 civilians and military personnel out of and into the city over 323 days (To Save a City: The Berlin Airlift, 1948-49, PDF), though that mission was not primarily an evacuation, and some figures cite the total number of civilians evacuated at 48,000.
For some context for a military airlift, the U.S. and allied forces moved 472,800 people -- presumably mostly military personnel -- to the Persian Gulf for Operation Desert Storm, over eight months following the Iraqi invasion of Kuwait in 1990.
As for the Indian airlift, the 170,000 figure appears to refer to the total number of Indians in Kuwait at the time of the Iraqi invasion. According to this 2014 article, some 111,711 Indians were flown from from Jordan to India over 63 days; it reads as if most were bused from Kuwait through Iraq to Amman, Jordan, where the Indian government arranged transport via the Air India airline. The Indian effort was dramatized in the movie Airlift (2016). (Different stories of the evacuation give different numbers for how many days the airlifts occurred and some count the total number of Indians in Kuwait needing evacuation as if they were all flown out by Air India.)
Various Indian sources say the Guinness Book of World Records cited the achievement as the largest evacuation of people by civilian airliner, though the Guinness site currently lists no records for airlifts by number of people moved.
As of August 28, 2021, the airlift out of Afghanistan by the United States and its allies had carried at least 117,000 people in 14 days, so that figure already exceeds the Indian evacuation.
Dividing the 111,711 Indians moved over 63 days and rounding up we get an average of 1,774 people moved per day; using the shorter 48-day timeline used by some puts the average at 2,328 per day. The allied airlift out of Kabul has moved an average of 8,358 people per day. (Dividing the Berlin airlift figure over 323 days gives us 705 people per day.)
(The airlift ended August 30, 2021 after moving more than 122,000 people, according to this statement by Army Maj. Gen. William “Hank” Taylor. The Washington Post dubbed it "one of the largest airlifts in history," which I think illustrates the challenge of defining "largest" in this context.)