How does tangzhong (water roux) make bread softer?
The tangzhong is composed mainly of gelated starches.  According to Harold McGee's  "On Food and Cooking"  


  During the baking of bread and cakes, the starch granules absorb
  water, swell, and set to form the rigid bulk of the walls that
  surround the bubbles of carbon dioxide. At the same time their swollen
  rigidity stops the expansion of the bubbles and so forces the water
  vapor inside to pop the bubbles and escape, turning the foam of
  separate bubbles into a continuous spongy network of connected holes.
  If this didn’t happen, then at the end of baking the cool- ing water
  vapor would contract and cause the bread or cake to collapse.


In the Tangzhong, the starches are already swollen before mixing begins.  This means that they do not need to compete with the proteins to absorb water as the completed dough warms up in the oven. As you mix the ingredients the plump starches perforate the gluten-water sheets.  As McGee mentioned, these starch granules' rigidity accounts for the spongy, close structure of the tangzhong crumb, dough with less perforated gluten mesh forms larger bubbles and a more open crumb.

The gluten in the flour used in the tangzhong is denatured by the process before it can form into an extensive network.  However, since the tangzhong accounts for only a small portion of the total flour used, there is plenty of gluten left to maintain structure during rise and oven spring until the starch structure sets.

Other resources:

Tangzhong Water Roux Pain au Lait: Soft, Springy Sandwich Bread