If someone can post a link to an image of the world, showing night-time flaring of LNG, I can add the image to the post.

how do they shut out all the rest of the light and just show the gas flaring??

I might have thought they would use UV emission lines characteristic of flames, but even if some of those emissions pass through the atmosphere, it would take a specialized satellite. Instead, according to the huge PDF that is the "report" linked on the NGDC Earth Observation page, it looks like they use educated guesswork. To oversimplify, a gas flare is apparently a bright light that appears in a generally unexpected place such as over water, is steady for a period of time, but not too many years, is generally round in shape, and is identified with substantial effort by human analysts rather than by fully automatic means. So the map is probably laboriously produced, and pretty good but not perfect.