Your screenshot points to an attempt to create a 2010 Empty project, but your text refers to 2013. I'm assuming that your working with 2013. The answer below is mostly appropriate for both however.
In 2010, you only had the option of SharePoint Projects - code that ran on the SP server. These are still available in 2013 (Empty Project, Visual Web Part etc.) To develop for this kind of solution you will need to have the appropriate run-time (i.e. SP2010 or SP2013 installed) on the development machine.
SP2013 introduced a new kind of project / model - the App. These solutions are not installed on the server but apply one or more config / library / list interactions via js/css and possibly other, off server web-services. These are called Apps. The MS documentation is generally consistent about this but it does require some attention when reading especially if, like me you can interchange app with project with solution.
So, to answer the question, the error message is correct - you are trying to start a 2010/2013 project without the runtime being installed on the same machine. If you'd like to develop a 2013 App then that can be done without the SP2013 product install but you will need a copy of the Office Developer tools for Visual Studio.
The MSDN Article has the 'important' clarification about Apps just below the first section
You can develop app for SharePoint solutions in Visual Studio 2012 if Microsoft SharePoint 2013 is installed on a remote server. However, you must install Microsoft SharePoint 2013 locally before you can develop other SharePoint solutions.