It works sometimes. That doesn't mean it's infallible or easy to interpret. I'm not saying it's a perfect system, or even a highly-effective one, but if you know what exactly it does and how it's supposed to work, it can be helpful. If you don't, then it won't do anything except confuse you.

Your quote:

If parts of the image are from different source files, they may have been saved a number of different times,

Maybe the photo was originally not a JPEG, and therefore the algorithm can't interpret it. Maybe the dude got lucky and ended up using two images that had a very similar number of saves. The point is that just because it has problems doesn't mean it's completely worthless. Newtonian mechanics is an imperfect way of describing the world but nonetheless happens to provide models which are very useful in the hands of someone who knows their limitations. Likewise, Google PageRank happens to be susceptible to all kinds of SEO schemes and gaming that lets sites appear far higher in search results than they should. Just because a tool has problems doesn't mean it's useless. JPEG error level analysis is ultimately a flawed but sometimes helpful way for someone who understands how it works to observe potential areas where an image has been edited, nothing more. It only becomes completely useless in the hands of someone who doesn't understand what they're looking at or assumes that it's a magical tool that can perfectly and accurately detect photo manipulation 100% of the time with no false positives.

Maybe you should read this part of the explanation, too:

It is worth noting that edges and areas red in colour are often depicted as brighter in the ELA tests. This due to the way the photos are saved by various programs. It is not proof that image was manipulated.

If you are unsure how to interpret the results, please do not claim the results of this tool as proof of anything.

In response to your last claim

The non-shopped images lit up like Christmas trees, but the clearly shopped one was silent, the explanation is rather simple really.

From the FAQ:

If the results from the ELA tool show an image which is all bright, it does not indicate that a photo has been manipulated (quite the opposite actually). What does indicate manipulation, is different levels of brightness throughout the image. If certain sections of the image have noticeably different levels of brightness, it is a strong indicator for further investigation.

And:

If a picture has been resaved many times, or if a picture is of a very low jpeg quality, it is quite difficult to determine accurately whether it has been digitally altered. Likewise, if all parts of a picture have been saved the same amount of times, it will not pick up either. This tool is set up to work on high quality jpeg photos (95% quality), and as such, if it is run against lower quality photos, the results can be harder to interpret.

Just because this tool does not show any sections of the image at differing quality levels, doesn't mean the image hasn't been manipulated. If all the source images are all of the same quality (or all of poor quality) then it likely won't show much.

edit: I should also note that this is meant to be used in conjunction with a variety of other tools. This is an article which shows ELA being used alongside direct inspection of the image for obvious mistakes, analysis of the image's metadata, JPEG fingerprinting, a luminance gradient and a high-frequency noise test. Relying on a single method is pointless, especially if you don't know what you're doing.