I've seen CIELab used to do color transformations, and it has a problem. This color space looks like it will suffer from the same problem.
If you try to shift hues, keeping a constant luminance causes a problem. You can't transform a bright blue to a bright yellow, because the luminance of blue is considered much lower than yellow. The best you'll get is a very dark brown.
Sometimes the goal is just to change the color of an object while retaining the shadows, highlights, and textures. Suppose you had a picture of a blue car and wanted to know what it would look like in yellow.
That example looks like it's working directly with RGB, which I expect to be correct. I've also seen it work well in HLS. But I worked on a tool where we were told to change from HLS to CIELab because it would be better, and it turned out to be much worse in practice.
I almost always use CIELAB as a working color space for photographic work (my action linked previously converts to 16 bit/channel CIELAB space as its first step, though you could use a similar type of tool in RGB mode if you wanted to). But I have a pretty good idea of the final RGB (or other) gamut I am aiming for.
Photoshop is definitely designed RGB-first, and some of the tools get a bit clunky in CIELAB mode. It is still an improvement for most of what I want to do.
I have many ideas for better image color manipulation tools.
If you try to shift hues, keeping a constant luminance causes a problem. You can't transform a bright blue to a bright yellow, because the luminance of blue is considered much lower than yellow. The best you'll get is a very dark brown.