I don't think your guitar cable will make a significant difference here. When I said "backing track" I was suggesting perhaps drums, as with the YouTube video. Guitar will sound very different when mixed with other instruments.
There may also be some post processing, like EQ, and compression at work here as well. Recording through a sound card's analog inputs will also give a somewhat different result that recording via USB.
One more thing worth mentioning. There are also mechanical factors involved. Your pick, pick attack, fingering style, muting style, pickups, guitar output volume, tone settings, are all variables in the mix that can change the sound.
I wsh you luck, but there is a lot more involved in copying and recording a particular tone than just amp and effects settings.