In order to present said alien civilization with an adequate definition of Modus Ponens, we would need to provide the truth values of both P and Q for every possible case, rather than just one or the other and for only some cases. (If we were to apply more generally your method of revealing only part of the output, we could avoid ever adequately defining any function because we could always keep re-iterating the premises (or just tacking on a tautology, such as (P or ~P)) in our output instead of providing any new information).
What distinguishes MP from the disjunction (P or Q) is that in the latter case, P and Q cannot both be false under the same interpretation, while in the case of logical entailment, it is not possible for Q to be false while P is true. This would be evident to your hypothetical civilization.
The mathoverflow post to which you linked covers efforts to get around the ability to draw unrelated tautological conclusions by attempting to set rules for a relatedness requirement--but this is mostly a matter of psychology, because formal logic does not purport to do anything except preserve the truth, and that it does. The efforts do, however, make logic more useful to humans because they create reasoning-like restrictions.
...P.S. As @Schiphol mentioned, the material conditional has nothing to do with causation. Rather, it dictates what IS true, right now, given that something else IS true, right now. Look up subjunctive arguments to see some truth-functionality issues with trying to bring temporal qualifiers into propositional logic. There are separate, temporal modal logics to deal with that sort of thing, because propositional logic is not really sufficiently expressive.