Without wanting to place too fine a point on it, the macro discussed in this thread is for use in documents containing formfields. Your document has no formfields; it has content controls.
For adding a new row to a table in a document with content controls, see:
Code to add new row in table
Macro to add row to table in a Word form
https://www.msofficeforums.com/word-...tml#post145675
The first of these has all you need.
There is certainly no need for a button on the QAT when using the correct code. The reason you needed one for the code in this thread is that you're not using formfields and, as a result, can't use their 'on exit' macro property to trigger the code; this isn't required for content controls.