Though you've given us little to work with I think this question has a simple answer:
I disagree with you that the request is neither a 'pure' query nor a 'pure' command. The request is a pure query, because the request is not a request for an analysis, but a request for information. The analysis that optionally gets triggered by the request is a command, but a command in the context of the query event. The system, or more specifically the event handler, is therefore the actor in the context of the command, not the user, which is the actor in the context of the query.
No query is ever side-effect free. It is the intention what makes it a query.