You may be shocked to see that the ORAC value of nachos ranks it along more respected foods such as navy beans and red grapes. The test reported that low fat corn tortilla chips made with olestra (1), which is an artificial fat substitute used in lieu of oil. It was more popular in the 00's and afterward its popularity faded as it got frowned upon in the same way people look at artificial sweeteners. The type of cheese used was not specified, so it's unknown whether it was cheddar or another variety, but if it were artificial (i.e. Cheese Whiz) the labeling would not have referred to it as cheese.
In terms of the antioxidants, we can presume they are coming from the corn. Meat and dairy contain very little. You can compare corn chips to corn flakes which have the same primary ingredient as nacho or tortilla chips and a similar ORAC reading.
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010