The English "it requires energy to work" unfortunately holds an ambiguity. As it can be an "it" that needs energy, this thing needs a source of energy to be working. That would be den trenger/krever energi for å arbeide/fungere/virke.
Or just your general "it" as in "it's raining", working requires energy. Det krever energi å jobbe/arbeide/fungere. "Fungere" is really not any more a synonym for "jobbe" than function is for work, but in this sentence it works (...).
Your assumption is correct. To me the sentence means that a person doing some kind of job will require energy in order to do so. Not necessarily just calories, but perhaps also being well-rested and avoiding other things that "drain your energy".
To do work in the mechanical sense is usually "å utføre arbeid [på noe]", I think.