Non celiac gluten sensitivity causes are not well understood but there are some ideas and this article will give you some clues.
One theory is that gluten, the trigger for celiac disease and gluten allergy, is also responsible for non celiac gluten sensitivity symptoms. It is also possible that other components of wheat, oats, barley and rye cause symptoms instead of or as well as gluten. Two of these are amylasetrypsin inhibitors (ATIs) and FODMAPs. 
Amylasetrypsin Inhibitors and Gluten Sensitivity
amylasetrypsin inhibitors. also known as α-amylase/trypsin inhibitors or ATIs, are types of pest resistance molecules in wheat. Studies show that they cause inflamation in the intestines of those with celiac disease, and some people without celiac disease. They also appear to cause inflammation in other parts of the body. There does seem to be a genetic component to this, although not necessarily the same genetics as for celiac disease. 
FODMAPs and Gluten Sensitivity
FODMAPs stands for fermentable oligosaccharides, disaccharides, monosaccharides and polyols. These are are short chain carbohydrates that are poorly absorbed in the small intestine. They appear to mostly cause problems in the intestine and are found in grains like wheat and other vegatables such as onion, beet root and cabbage.
 Nonceliac Gluten Sensitivity, Alessio Fasano
 Wheat amylase trypsin inhibitors drive intestinal inflammation via activation of toll-like receptor 4, Yvonne Junker et al
Wikipedia on non celiac gluten sensitivity