The simple past can be used to describe a single event in the past. This makes the meanings of "...because he drove" and "...because he was driving" very similar. There is a slight difference in viewpoint (whether the fast driving was a single event or a continuous process) but this is minor. I would tend to use the past continuous "...was driving..." because the process of driving fast took longer than getting a ticket, and he was stopped while the process was ongoing. Compare
John was arrested because he shot Sally.
(not "was shooting" we are talking about a single event not a process)
Similarly in the main clause "John was driving" and "John drove" indicates we are thinking about the event slightly differently:
John drove to the shops
John arrived early at the party because he drove.
It was an event
John was driving to the shops (when his tyre burst).
It was an ongoing process that was stopped by a short event.