" I(X;Y|Z) is interpreted as `` the reduction in uncertainty of X due to the knowledge of Y when Z is given."
Would it make sense when talking in a geographical sense to say :
When information flow in the EU (Z) occurs the flow of interaction between the countries (I) increases due to labour flow (X) and capital flow (Y) being more dependent than before?
So I(X;Y|Z)>I(X;Y)
And also if it does make sense, which it probably doesn't then could I just add another variable to it so that V= flow of goods?
I(X;Y;V|Z)>I(X;Y;V)
Would I be saying that the interaction within the EU is larger when information flow occurs because when it does flow of goods, capital and labour are more dependent than without?
I cannot say if the concept of conditional mutual information $I(X;Y|Z)$ has any relation to your geographical/political situation. (I'd say it has little or no relation).
Anyway, notice that the inequality you are trying to apply $$I(X;Y|Z)>I(X;Y)$$
contradicts the interpretation given: if it's a "reduction in uncertainty of X due to the knowledge of Y when Z is given." then the inequality should be reversed.
Furthermore, the inequality (in any sense) is just wrong, as the above interpretation. The conditional information can increase or decrease when conditioned to another variable - this elementary fact is mentioned in the Wikipedia.