To be clear, it is unknown for sure whether the USDA used Nesquik brand for this test. However there is good evidence to suggest they did. If you look up the ingredient number they disclosed for this (14192) and pull it up in USDA National Nutrient Database, you will see they report it as "Beverage, Cocoa mix, powder" with 18.35 grams of sugar per serving (with 1 serving = 3 heaping teaspoons weighing 28 grams). This is quite similar to what you will find on the container's nutrition facts label. But whether it was Nesquik vs. Ovaltine or Nastle Milo, they all have very comparable ingredients and therefore, we would expect to see similar amounts of antioxidants in each.
So how does the antioxidant content in powdered chocolate milk mix compare to raw cocoa powder? The difference is night and day. The ORAC value of 100% pure cocoa powder is 55,653. That's over 100 times higher than the heavily processed chocolate flavored mixes with sugar.
Does this mean dry chocolate milk mix isn't healthy? Well, we certainly wouldn't consider it a high source of antioxidants. For that you would do better buying some raw cocoa powder and adding it to a milk of your choice, whether that be dairy or vegan milks like almond, soy, and flax (on that note, as of 2016 Nesquik powder is vegan apparently, as the ingredients no longer list the cow milk derivative capolac). Making it yourself would also allow you to cut out the added refined cane sugar and instead, substitute it with a lower glycemic sweetener like maple syrup or better yet, monk fruit or stevia if you are dieting and want zero added calories.
The other advantage of creating your own powdered chocolate drink is that you may have better control over the amount of acrylamide it contains. That's a substance which is a classified as a Group 2A carcinogen by the International Agency for Research on Cancer (IARC) which is part of the World Health Organization. It's created when carb-rich foods - such as cocoa beans - are roasted. By making the mix yourself, you may be able to avoid acrylamide to some degree by using unroasted cocoa in it.
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