I love ambition but the YouTube video is doing something much more simple than what you seem to be planning. He is sending some power to a single white LED based on what comes out of his audio feed... something that could be done just as easily, if you wanted to, by placing LEDs directly into your speaker terminals (+ / red and - / black) - then you'd soon get the LEDs flashing to the music... you might well fry a few LEDs at higher volumes or with different amplifiers, but you can place resistors in there easily enough once you figure out the limits (by guessing, I mean... that's what I did, I'm sure there's a more 'science' way to do it)... but start out at low volume. I never broke anything important (like my amplifier or speakers) by trying this out - but others more knowledgeable might scream at me.
What you're actually thinking of is connecting an audio source straight to an RGB LED controller... but what are your expectations from this? Do you expect the LEDs to light up at different intensities of white, i.e. R, G, and B will all get the signal from your audio input, or are you actually thinking of getting the LED strip to do really funky stuff based on what the music is? By that, I mean different colours for different frequencies, cool chasing patterns (seems your LED strip is quite advanced) etc.? I can't see how it ever would do anything smart like that with just the bits you have shown and what is in the YouTube video.
I do hope you get somewhere with this, as I would love to see the results, but I do not think that replacing the single white LED the guy is using in the YouTube video with your RGB LED controller board is going to get very far... it seems a whole lot more complicated, to me... it seems, to me, that you might have to end up writing your own stuff with a micro-controller.