Music is really subjective - and I'm not aware of a way to quantify the impact of music generally. The same challenge applies to a musical "artists", but justification of the skills of DJs is often demanded, where the skills of artists isn't. Why is that?
From the perspective of someone who had gone through the learning journey, I know full well the difference between my abilities when I begin and now (and there's still a lot of space for me to improve). Those first times I DJed were fairly horrible experiences for everyone - most of all me.
What can we figure out though? There are really just a couple of main dimensions to consider, song selection and how those songs are put together.
Song selections are crucial to DJing and you can think of it in terms of tailoring the music to the environment. Whether you have 2 turntables or not, this is the most important part. Maybe you have a someone putting on other people's mix tapes - understanding the energy and environment are still crucial. I've seen people who are accomplished musicians get this very wrong. It's not something that comes of being a good musician, it's a totally different skill-set.
So before you even look at the medium (turntables), I think we can agree that there's a skill involved in being able to apply music to enhance the environment.
Then there's the turntable aspect. If you give someone with the skills to apply the right music an infinite supply of music and an mp3 player they'll struggle to make the experience smooth. A pause in the music is going to kill the energy in the room. But that's just the start. You can change the energy just by moving through tracks faster, before you even start looking at the interesting ways you can put the music together. Not only that, but pretty much every DJ setup these days is digital with much more you can do to the music in the mix.
It's like lighting - take a perfectly good party and put strip lighting in. It's all about creating the right environment. Music is a big part of that - though I suspect I'm more aware of it than other people.