HBridge short circuit between switches
I'm hardly an expert on the subject, but the idea seems to be to better approximate a sine wave by having a period of 0V between the peaks. The explanation is in the document you cite:


  The major problem with the push-pull approach [they are talking about a straight-up square wave here] is that the current in the transformer has to suddenly
  reverse directions. This would be like shifting your car into reverse at fifty miles per hour. This
  causes a large reduction in efficiency as well as potential for large transients, thus degrading the
  waveform.


Then they introduce the "Modified Square Wave":


  The addition of an extra winding in the transformer along with a few other parts allows output of a
  Modified Square Wave (often referred to as a modified sine wave by marketing types) while still
  utilizing a push-pull topology (Figure 5).
  
  The switching cycle is identical to that described in the section on square wave inverters, except for
  one additional step. In the switching cycle, another step is added which “clears” out the transformer
  reducing the problems associated with the sudden change in current direction. This is accomplished by
  the off time shorting winding shown in figure 6.


Up to this point they are only talking about a push-pull topology. The section you ask about is then describing the same technique, but with an H-bridge topology.