Actually (as in older version) moving a question in another category is done by modifying the question->category parameter as in
line 486 of question/editlib.php
if (!set_field('question', 'category', $tocategory->id, 'id', $questionid))
Calculated question can use category shared dataitems sets and just changing the category is not sufficient.
I suggest that a moving_to_category() function being created in questiontype and that the default function could be the one used.
I let you create the function and I will work on a specific one for calculated question.
I suggest that the entire list i.e. $questionids be passed to the function because if you move all or part of the calculated questions that are in a category, the moving process is different.