You will not be able to get any more than an image of the pivot table into an HTML report. There are other options.
First, you will need to clone the pivot table object in QlikView and change that to a straight table. You can hide the cloned object or place it on a hidden sheet if you don't want to expose it to your QlikView users.
From there, follow the process to import the pivot table into an Excel template and recreate your pivot table there: How to Create a Pivot Table Report with QlikView Data
Then when you set up the task, add the Excel template but choose HTML as the output format. This will allow you to embed the report into an email.
In NPrinting, there is no out of the box solution to manage building a pivot table in HTML template editor other than as you mentioned - dragging the Pivot object in as an image.
If you do a google search on "HTML pivot table",you may be able to find a solution/structure to do this. You likely would need to use QV straight table data (clone and convert your pivot table to a straight table) in order to build an html pivot table solution.