You have answered your own question.
It works only if the system have skype installation
That is how it works.
The Skype API need to be there inorder to make calls right ?
If they don't have Skype, you can tell them to get it from the website like this
<a href="skype:echo123?call">Call the Skype Echo / Sound Test Service</a>, If you don't have Skype installed. Download it from <a href='http://www.skype.com'>here</a>