On further investigation I realised that only the files supported by Windows Media Player did not show the Enqueue in Foobar option.
Though the usual solutions to the problem involve registry modifications, I found a very simple solution to it.
First make sure the Folder Context Menus option is checked in the Library>Configure>Shell Integration in Foobar.
1. Go to Control Panel > Default Programs > Set program access and computer defaults
2. Choose the Custom configuration.
3. In the section Choose a default media player uncheck Enable access to this program for Windows Media Center and Windows Media Player.
4. you’re done!
The “Enqueue in Foobar” option will be present in the right-click context menu of all audio files now. 🙂
Thanks to http://www.uberullu.com for the tip.