Please uninstall everything:
(1) ArcGIS Desktop 10.2,
(2) ArcGIS Engine 10.2,
(3) ArcObjects SDK for .NET 10.2,
(4) Microsoft Visual Studio 2010.
Restart your computer. Then install the software in the following order:
1) ArcGIS Dekstop 10.2
2) Visual Studio 2010
3) ArcObjects SDK for .NET 10.2
4) ArcGIS Engine for .NET 10.2.
Make sure you have licensed your ArcGIS Desktop with either a Basic, Standard or Advanced license. Also, you will need to license your Engine installation with a Single Use Developer Kit license.
Then try to create an Engine application (from File | New Project | Visual C# | ArcGIS | Extending ArcObjects | Console Application(Engine) . You should not get the error again.