Only Asterisk has direct support from EPESI. Even skype integration is not provided solely by EPESI, because Skype has a browser plugin, that handles callto: protocol. Phone numbers are changed to callto:<number>, then Skype is able to recognize them and creates links to make a call.
Asterisk integration in done differently. Phone number is a link - when you'll click on it, asterisk server will initiate calls to you and your destination.
If you're interested in certain skype alternative, try to find if it has browser plugin to support callto: protocol.