WordPress Insert line in DB when clicking a button

There are many problems here. Resolving one leads to another.

Uncaught ReferenceError: response is not defined

In your JavaScript code, you set the success key to a function

function (data) {
    $("#result").html(response);
}

• response is not defined. The callback has a function parameter of data, not response. This causes the error.
• .html(…) sets the HTML content of an element. data would not be a reasonable variable to use since it is not HTML.
• Returning something useful from the PHP code would provide no value without an element matching the query selector #result.

Therefore, delete the line $("#result").html(response);.

Then your function would still not be called. Making a request to process.php would declare the function but not call it. You need to actually call the function you declare, ButtonPubVideoHdp_InsertData(), in your PHP.

This is not the right way to make AJAX requests with WordPress. Please follow the guidance at:

• https://codex.wordpress.org/AJAX_in_Plugins