I think I understand where your confusion comes from, and the reason for your question.
When we talk about a supervised problem, it means that there is some feedback of how well the machine did at a certain task. Of course, we always need this kind of feedback in some way or another (otherwise, the machine would never learn, because it would have no incentive to change anything that it does), but the feedback can be classified into "supervised" if we have a clear way of telling when something was right/wrong, or "unsupervised" if we just roll out with the results and try to make it better each time.
For example, an AI performing translation like in grammar induction in the other question will take as input both the phrase and the syntactic tree. After performing the prediction of what the syntactic tree for the phrase should be, it can be compared against the real syntactic tree given as input and based on the accuracy of the prediction, the weights (think of it as "knobs" that adjust the result) can be tweaked a little bit to give better predictions next time.
This type of learning is considered supervised, not because of the existence of a supervisor, but rather because there is labeled data that we can use to test predictions and better them next time.
Unsupervised problems don't have this kind of labeled data, and just work with what they have. They cannot tell what's right and what's wrong in terms of predictions, they only have raw data and try to make sense out of it by extracting correlations or common properties.
For the case of a language, I will go on a limb here but I'll say that this is mostly likely a task for supervised algorithms. Unsupervised techniques could properly analyze language and determine that they actually have a particular structure, but this is also true for lots of other sources of data that are not language. An alien race, knowing nothing about humanity, could end up deducting that cars honking are some sort of language too, albeit much simpler than human-produced noises.
Also, the natural flexibility that languages have make it extra complex, because they don't follow a correct structure completely, and to make it worse, they are constantly changing.
As leitasat mentioned in their comment, if even human scientists (which we certainly deem intelligent) could not decipher ancient Egyptian on their own without any context, it's very unlikely that a machine would do it.
Finally, notice that translator machines or inference machines don't actually derive meaning in a way that's meaningful. Without going much in much detail, you should think of them as "correlation detection machines" -- so a machine might notice a high enough correlation between how "Hola" is used in Spanish as to how "Hi" is used in English, and by giving you that information, we call it a translator. However, the internal learnt structure is actually just a probability distribution for an output given a set of inputs.
Not to say that any of this is not useful -- it definitely is -- but with something as separate as an alien race of super-human intelligence and without any way to derive meaning from just a bunch of sounds, it's very unlikely that a machine would prove useful in such correlations.
And still, I cannot find any hard stop to your idea -- if these aliens have a language and they express the same concepts that human express, then there is correlation. There just needs to be a way to find it.
Sorry for the wall of text and the huge rambling, I hope I provided some context on the points you were looking clarification for.