The real distinquishing feature of formalism is that everything has a definite character. There are no half-steps or in-between states. This is not to say that modern physics with the indefinite states that are the superposition of many states is not a formal system.

When we say that a system of currencies is a formal systems, we are saying that there are a set of rules and axioms that describe the possible transitions of the system and how one state evolves to another. The analogy to the rules of a game can be more than an analogy as we design a framework for currency systems as a set of open and formal protocols.