I have always seen an Airshow is where the primary entertainment is aircraft displaying and an aircraft is deemed as displaying if it performs a routine rather than a simple flypast. I would say a flypast of any sort is not an airshow at all as long as the aircraft did not perform more than one or two passes. I assume the latest CAA changes would not have an effect on situations where an aircraft performs a fly past possibly as a tribute event or events such as fetes, country shows Etc.

Many events are a bit of a cross over such as Wings and Wheels events then we have Goodwood Festival of Speed and Revival, have an air display element but are primarily a motor racing event, but in these cases the aircraft are performing a full routine, so that to me would count as an Air display and therefore an airshow of sorts.
Not sure if that makes the mud any clearer or answers your question.