Assuming those estimates are correct (I haven't verified it), I think it's hard for me to believe that there are fewer than 191K people working to manage an equivalent number of financial transactions in USD.
I tried this wolfram query: http://www.wolframalpha.com/input/?i=number+of+people+workin...
Yes, we are increasing entropy outside of ourselves but not within, if the population of humans is increasing, humans have acquired more negentropy from the environment and are "winning" against entropy as they get better at extracting energy from the environment, we'll run out of energy in the form of fossil fuels soon, so we'll have to find another source of energy, because we need more energy to decrease entropy.
Let me be clear(er) in saying that I don't support burning fossil fuels, I think OP linked mining bitcoins directly to burning coal -- we're mixing two very separate arguments here. Burning fossil fuels for generation of electricity is a topic on its own.