Indeed, the wording of the article even made me think of type theory and functional programming.

For instance, a kettle with a power supply can serve as a constructor that can perform the task of heating water.

kettle power_supply water : (water * heat)

You simply say that the task of creating energy from nothing is impossible.

first_law : (Null -> energy) = _|_

In principle, everything possible in our universe could be written down in a big book consisting of nothing but tasks

This sounds like an enumeration (eg. a Goedel numbering) of programs, or alternatively of a (program, runtime) quarter-plane.

The collaborators then go on to define the concept of a “superinformation” medium that encodes messages that specify particular physical states—in this case, one in which copying is impossible

Sounds like substructural type systems and linear (or affine) types.