Sound travels in waves, which are simply variations of pressure in a medium—whether solid, liquid or gas. The energy from vibrating objects, such as speaker membranes, moves from particle to particle in the air in a repeating pattern of high- and low-pressure zones that we perceive as sound. According to the ideal gas law, temperature, pressure and volume are related; therefore, a decrease in pressure can lead to a corresponding decrease in temperature, which may explain how sound can extinguish a flame.
Like most readers and the journalists sensationalizing this story, I don't have much understanding of the laws of physics that apply here. But it made me curious to ask those who know: Does it stand to reason that altering the frequency appropriately could increase air pressure or otherwise be used to create more ideal conditions needed for fire?