The kolmogorov-complexity tag was initially applied only to what you might term pure Kolmogorov complexity questions: those which asked for a constant output. Its scope has expanded over time, and I have also felt that its application to some questions was overbroadening it. However, to limit it to constant-output questions would be to overnarrow it.
A couple of quotes from Wikipedia (my emphasis):
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of the shortest computer program (in a predetermined programming language) that produces the object as output.
The broader area encompassing descriptional complexity and probability is often called Kolmogorov complexity
To restrict the tag to constant-output questions (understanding output to mean strings or byte sequences, since writing to stdout is one of our standard output options) is to discard other objects. And to insist on the narrowest possible definition of the term KC is to put pedantry ahead of the value and purpose of the tag system, which is to enable people to find questions of interest to them.
IIRC one of the earliest non-constant-output questions to be tagged kolmogorov-complexity (and it turns out that I was the one who tagged it, although I didn't remember that when I went looking for it yesterday) was Who's that Pokémon? It takes one input, an integer, and gives one string as output. There's no mathematical formula which will get the output from the input.
This question could have been written as follows:
Write a function (not a program) which takes no input and returns an array of these 151 elements in this order: ...
Is there any good argument that this rewrite doesn't deserve kolmogorov-complexity? Sure, it's a function rather than a program, but that's only because a program can't output an array but only a string representation of an array.
Or can it? By taking the array index as an input and giving the corresponding element as an output, answers to the question as written are essentially managing to output an array to stdout. So although on a very narrow definition this question might not be KC, there's a strong argument that it's actually asking for the KC of a non-text object even on a fairly narrow definition, and I don't think it's possible reasonably to argue that it doesn't fall within the "broader area encompassing descriptional complexity" mentioned in the second Wikipedia quote.
 Ok, you pedants, except a case-wise definition.