.vap files need to be imported from VoiceAttack's GUI. Windows won't "know" what to do with this file type.
Click the
icon on VoiceAttack's main window, choose "Import Profile", select the file you downloaded, and click "Open".
Note that .vap files only contain data on how to reconstruct a profile into VoiceAttack's profile database. After importing, the .vap file is not used at all, and can be moved, or even deleted if you don't foresee needing to import it again.