Well, if you come to this page from Google, I believe you are working on demo environment of your SharePoint and try to install Application Templates from Microsoft, and you're kind of puzzled and stress, why the Application Templates cannot be installed, as you have done it smoothly in your own VPC.
Well, one of the possible reason is ApplicationTemplateCore is not installed yet on your server farm. It's one of the initial step before you use any Application Templates. Having played and installed so many application templates, people might miss the initial step in the other SharePoint environment. If this is not the case, there's other suggestion that might work is to append "-force" when you deploy the solution.