FileMaker is a solution development tool and the Email Campaign Management starter solution is just that. It's a starter solution to show how you might go about using FileMaker to manage Email Campaigns.
Inside this starter solution, you have a script for sending emails. From your description, it's designed to send one email at a time not to groups of recipients with a single mouse click. You'll need to find this script, learn how it works and then develop a new script that does the same actions but which you've modified to send email to groups of recipients.
Depending on how the script currently works and what you need it to do for you, this may be a very simple change or one that takes a bit more scripting to do.
One issue to look out for: You can send an identical email to multiple recipients or you can send customized emails where the message has been personalized, one email per recipient for a selected group of recipients. How you do it in each case is different--so make sure you know which result you want beore you start making these changes.
Thanks once again. This is really helpful.