Please run it from the terminal and give me the output:

skypeforlinux

Well, there is no output, see screenshot:

http://i.imgur.com/RGrm4UV.png

Literally nothing happens.

I had the same issue, try install libxscrnsaver.

works fine for me, but as kostaswl states i do have the libxscrnsaver package...

$ eopkg li | grep -i scrnsaver
libxscrnsaver - X11 Screen Saver extension client library
libxscrnsaver-32bit - 32-bit libraries for libxscrnsaver

Thanks for that, Skype works after installing libxscrnsaver-32bit. But shouldn't Skype pull this package since it is required for it to work?

But shouldn't Skype pull this package since it is required for it to work?

I believe it requires libxscrnsaver, not the -32bit (I'd be surprised if it was needed, anyways). The commit I made specifies libxscrnsaver as a rundep and updates Skype.

But I had the libxscrnsaver package installed, and it didn't work. Only after adding the 32bit version it started working fine.
Anyway thank you for solving this issue.

Gotcha, I'll add the -32bit too for good measure.