If a module has only two terminals, but has some parallel LEDs internally, you can probably assume there's something inside the module to balance the current between each parallel circuit. This is made somewhat easier when all the LEDs are in one module because they can share a heatsink, and thus the temperature of each is likely close, and temperature variations are a big factor in why parallel LEDs will not share current equally. Each LED was also likely manufactured at the same time, so have very similar characteristics, which you can't guarantee when taking discrete LEDs out of a jar. The module may also include some small resistance in each parallel circuit to help balance. Point being: assume the manufacturer has taken care of this, and all you need to worry about is supplying the correct current to the two terminals provided by the module.
Your particular module is really like three modules, one for each color. It looks like there is one common terminal on the bottom, and three separate terminals on the top, one for each color. I can't find a datasheet that specifies if the cathodes or the anodes are common, so you may have to figure it out for yourself. It looks like maybe you can cut the common terminal apart if you want, but again, I see no datasheet, so you might have to experiment for yourself.
There is no special kind of LED driver that can drive parallel LED circuits. If an LED driver's job is to pump electrons, there's no way for it to tell some electrons to go down one circuit while telling others to go another way. The electrons decide which way to go by going whichever way minimizes their potential.
So, what you want to do with this module is power each of the R, G, and B sub-modules with a suitable driver (or if you can find it, one box that actually has three drivers in it). What you don't want to do is try to put the R, G, and B sub-modules in parallel and drive them all together. Since each color has a different forward voltage, this won't even remotely work: the color with the lowest forward voltage (red) will take very nearly all the current and all the power, and possibly be destroyed. At best you just won't get the other colors to light.
There is already a solution to converting stereo audio to a digital optical signal and back again that's widely used and readily available: TOSLINK. It basically is a simple conversion from the electrical S/PDIF signal to an optical format. There are many commercial chips that can convert directly between analog audio and S/PDIF (in both directions).
The only difference is that TOSLINK normally uses inexpensive plastic fiber to couple the light between the transmitter and the receiver, and you want to do a "free space" transmission. Therefore, you are going to have to focus on the optical part of the link, dealing with highly-variable signal levels and lots of potential interference.
White phosphor-based LEDs tend to have poor frequency response, mainly because of the slow decay of the phosphor's glow, although if you read datasheets carefully enough, you can find some with fast phosphors.
But you could use the slower LEDs if your receiver includes an optical filter that passes the blue light directly from the LED and ignores the yellow light from the phosphor. This might be a good idea in terms of rejecting interference anyway.
Best Answer
I have a similar project, using a high current LED driver IC and a separate PWM generator.
At these currents, linear regulators are too wasteful and would run too hot (a LDO with just 0.4V overhead would have to dissipate 40mW), and you need fairly exact current control, so most of these driver ICs use a buck or buck-boost topology, with external inductors (plus flyback diode) and capacitors.
I'm using a quad-channel driver, the LT3476 in combination with an LT8500 PWM generator. For you, a triple-channel driver might be better suited (I have RGBW LEDs).
The datasheets include an application note that includes a schematic and rules for component selection and board layout. It's still an intermediate level project, but doable.