DPI, or in this case actually PPI, is independent of picture quality and pixel size of photos. It specifies how many pixels of the screen fit inside an inch of the screen. The camera will keep on taking pictures at whatever pixel size you specify it to, and the screen will still show the same number of pixels - it just has a different idea of how many pixels on the screen are an actual inch on the screen.
What changes is what happens when an app is coded to show, for example, a letter that is specified to be an inch high: the screen will show it at a height of whatever the DPI is set to. Apparently, the FP2 reports a dpi of 160 pixels, which should actually be 446 (the other way around, the app thinks it is actually drawing to 13.8 inch screen). The letter is therefore displayed at 160/445 = ~0.36 inch in reality (which leads to problems such as this). Note that in this case there are fewer pixels used for the letter, but only because it was specified to have a certain physical size. As the pictures aren't defined by physical size when they are created, it won't affect the quality.
The reason that the PPI for the FP2 hasn't been fixed is because it seems to break Google apps compatibility testing. See this topic for more info. People have changed the PPI of the phone manually to 430 or 445 from the current 160 (note that this does require rooting the phone) and I haven't read of any adverse effects.