Here's the corresponding opensuse bug https://bugzilla.opensuse.org/show_bug.cgi?id=988273
From what I understand it's identifying the statically linked openssl as causing the issue with no workaround if the distro is to continue using up to date openssl (as most distros do). Hopefully Valve will action this bug (please!).
Fixed in openSUSE Tumbleweed 20160924.
Closing per the last comment.
Your system information
Please describe your issue in as much detail as possible:
Just tried to log-in, pretty much. More is described in the links (managed to dump output produced by Steam from launch to SegFault; where I should put the minidumps?):
https://gist.github.com/MGM175/70482e66fb26f7e42324f83e5f04204c
Steps for reproducing this issue: