Airbus have three window layers, so I assume the 737s do too.
The inner window layer is just window dressing, literally. It is only there to hide the fittings of the real window.
The middle layer and outer layer are both designed to handle the pressure. You'll see a small hole in the bottom of the middle window to deal with condensation and pressurization differences. I think the middle window does most of the grunt work in resisting the differential pressure. The outer pane is typically flush with the aircraft skin.
The photos in the article look more like delamination than an actual break, but it is hard to tell from the photos. I don't know how thick those panes are or if they are laminated.
What is odd, is that the window in the article is in a location similar to the other Southwest plane that had a window blow out. Probably just a coincidence.