Several reasons come to mind.
1. Population density
Air pollution is mostly caused by people and the more people live together in a particular area the higher the air pollution generally is. If people are spread more evenly over an area, so is the pollution which means that overall pollution levels are lower.
Both China and India have several cities in the top 20 of largest cities in the world sorted by population-density, for example Mumbai, Kolkata, Shenzen, Delhi and Beijing.
You can see that Delhi and Beijing have a similar density, but Delhi has a much bigger population so more air pollution is to be expected.
The first US city on the list is Los Angeles (position 90) with a population density only 1/4 of that of Delhi.
2. Number of cars
Traffic is a notorious contributor to air pollution, especially if you are measuring particulates, which the WHO study did. Common sources are exhaust fumes from fossil-fuel engines and dust from unpaved roads.
Based solely on population density you'd expect Mumbai or Kolkata to be the most polluting cities, but Delhi has by far the most vehicles of all cities in India: 7.35 million in 2012 which is about 2.5 times more than Mumbai (source). Beijing has an estimated 5 million cars in 2011 (source), Shenzhen about 3 million (source)
Areas with relatively low-income usually have more air pollution. This has to do with not being able to afford cleaner alternatives or filtering systems for manufacturing, travel and energy production.
Per capita GDP in Delhi is Rs. 210,000 (source), which is about USD 3,150
Per capita GDP in Mumbai is Rs. 486,000 (USD 7,300) (source)
Per capita GDP in Beijing is CNY 99,214 (USD 16,150) (source)
Per capita GDP in Shenzhen is CNY 149,500 (USD 24,084) (source)
4. Local conditions
Local conditions can play an important role, for example coastal cities usually have lower pollution levels compared to more in-land cities due to more windy weather (pollution is blown away) and the fact that there are less nearby polluters (no industry on the water).
5. Air pollution laws
I'm no expert on this, but it's been my impression that air pollution laws and regulations are stricter and better enforced in the US and China than they are in India.
Remarks about the WHO study
The WHO study did not investigate all cities in the world, but about 1600 cities for which data on PM10 and PM2.5 particulates is available. Many cities were not included simply because there is no local monitoring system. There is no data from most large cities in Africa, and very little from South America, Russia and the Middle East. So, it's possible that there are cities that are even more polluted than Delhi.