Can you take a closer picture of where the plug attaches to the LED strip? Chances are those are just plain old RGB strips (looks like 4 connectors, which would be +/R/G/B; the question is if + is 12V or 24V). I skimmed the kickstarter (lots of "science of the human eye" bullshit that makes it sound like a joke), and it looks like these are not individually addressable LEDs on a single strip, but multiple short single-color RGB strips you tape up around specific places on your TV.

You can likely do a couple things:

1. If you just need more length, you can take some regular old telephone wire (as long as it has four wires), cut it to whatever length you need, strip back the cut end, and solder the wires to the LED strips. Just make sure you match up the pins in the crimped end with the pads on the RGB (look at one of your existing cables; don't worry so much about wire color as position).
2. If you wanted longer strips of color, figure out whether it's 12V or 24V (I'd guess it's 12V, because the runs are short and 12V LEDs are cheaper), get a big ass-roll of RGB LEDs, and cut however long a strip you want. Then solder them to the existing cables, or per #1 make new cables.

LEDs aren't rocket surgery. The brainbox here is figuring out, "Quadrant X should be [RRR, GGG, BBB]" and sending that signal out over the RJ11 jack. All you have to do is be halfway competent at soldering and you're golden.