It would seem electron_utility.node in the latest versions of Skype requires GLIBCXX_3.4.21. Whereas, other components require no more than GLIBCXX_32.4.17 or less. If you are running a 5+ year old build of Linux, the 4.x GCC build provided will likely contain GLIBCXX_3.4.19 or lower. The solution is to upgrade GCC (5.x+) or obtain a newer build of that file from an app that is probably from an outside repository.
To get it to work on my clean test build with all available updates from its repository (CentOS7 from CERN), I believe I did the following with sudo. This guidance should work on other Linux builds.
1. Installed Skype disabling the gpg check for the rpm.
2. Modified the permissions for the Chrome Sandbox (sudo chmod 4755 /usr/share/skypeforlinux/chrome-sandbox).
3. Installed a newer copy of libstdc++.so.6 supporting GLICXX_32.4.21, into $HOME/lib. libstdc++.so.6 [pcdust.com]
4. To not have to specify a change in the LD library path via shell or shell script, created a Skype.conf file including $HOME/lib into /etc/ld.so.conf.d/ skype.conf [pcdust.com]
5. Executed ldconfig to record the change.
6. Launched Skype normally as displayed below.
