Nice question, reader Bob. Milk powder does a few things in baking application. First, it adds protein, and that along with the extra sugars can be handy if you want a darker, more golden crust. Powdered milk also adds flavor, another nice feature, especially for fast rising breads like doughnuts and white loaves which tend to be bland because of the extra-quick yeast action.
However the big benefit of dry milk is tenderness. The fats and the milk solids undermine gluten formation, which is always desirable from a texture standpoint. However foiling the action of gluten has other benefits for doughnuts, especially raised doughnuts. For instance, if the dough isn’t terribly elastic then the bubbles in it tend not to get very big. That’s good because a big open crumb can be a pain in the neck when you fry. The big open spaces can push the expanding doughnut out into weird shapes, or create giant open cells which can break open and fill with oil. Those big cells are also inconvenient if you’re filling your doughnuts with jam as all the filling tends to pool up in one place. In general in a yeast doughnut you want a fine, fluffy, even crumb. So you see there are a lot of good reasons for milk powder in a doughnut dough.
I should add that the finer your milk powder, the better, as the solids and fats spread out more evenly through the dough. That translates to a finer structure that is at once more tender, fluffier, taller AND stronger. King Arthur milk powder is especially fine and I heartily endorse it. Thanks again, Bob!