The article talks about "gliding", but that is so misleading. There is almost no atmosphere in space, so gliding is impossible. The more correct terminology should be orbital maneuvers. There is no need to "maintain guidance" as the article has emphasized.
The bouncy trajectory should not be viewed as a trajectory, but rather, an orbit. Hohman transfer is often use to raise the altitude of orbit. To perform such a transfer, one basically fires the engine at no place other than the perigee and apogee -- two points of an orbit that is closest and furthest from the Earth's center. It is the most efficient method possible to change an orbit.
Of course, firing the missile's engine off apogee will no longer be considered as Hohmann transfer, but doing it very close to the apogee and one can still gain an efficiency advantage. In the case of the graph, the engine is fired for a brief period just beyond apogee. This creates a new apogee ahead of the missile to take advantage of. The engine fires again for a brief period beyond the second apogee, which creates a third apogee ahead of the missile.
Essentially, this improves the efficiency of the missile by artificially creating a series of apogee for Hohmann transfers. For the same missile, let say DF-31, flying a standard trajectory and the maximum range would be 8000km. Flying the new trajectory however, could increase the range to 12000km.
Of course, there are some draw backs. To take advantage of this, the missile having solid fuel will either need to have three stages, or two stage with the second stage being liquid engine. But I am almost certain that the latter will be used, since a liquid engine allows one to turn on or turn off the engine at will, offering more flexibility for the user and unpredictability for whomever on the receiving end.