OK. The template is fine. It is the use that is the problem.
To create a new document based on a template, you need to double-click on the template icon or use File > New and locate your template to use. This is at least one layer more difficult in Word 2013. Read File New Variations in the Versions of Word for some methods that can make it easier.

BTW, I think you want to restrict editing on your form, at least as a starting point. You can add exceptions for each of your content controls. That will make it easier for you to complete.