TLDR: No, It does not. You can set your DPI to 75 or 300 and it will not matter.
To put it bluntly, DPI (Dots Per Inch) has no meaning when matching digital artwork to digital screens.
DPI is a concept that is very important when preparing digital artwork for print (including vinyl billboards). The size of a printed piece (as a subset of all physical objects) is measured in physical dimensions (like 14'x48'). DPI is the multiplier for converting those target dimensions to pixels (Dots Per Inch -- a pixel is a dot).
It's best to think of a digital billboard as a massive computer screen.
To take full advantage of a screen's resolution, you simply make artwork that has the same number of pixels (width x height) as the target screen.
In summary, a high DPI is important for print jobs. But, because all of our boards at Blip are digital, we work with pixels. No matter what the DPI of your image/artwork may be, any digital system simply put the pixels your image contains onto the screen. To optimize your artwork for any digital screen, simply match the number of pixels in your artwork to the number of pixels on the output device.