Perhaps worth noting that earlier in the document we defined acts as functions from world states to outcomes

I could not find a definition of "world state" in the document. All you say is

a state is a part of the world that is not an act (that can be performed now by the decision maker) or an outcome.

which is by no means a good definition. It tells you what a state is not, but not what it is. It even fails at that, given that it uses the term "part of the world" without it being previously defined.