I think that the open source driver not yet powerful enough for gaming. I'm able to play saints row series, bioshock and some indies, but not This War is Mine. It crashes a lot. So I switch to Catalyst proprietary driver and everything is fine

@ chui2ch

Take a look here: https://www.reddit.com/r/linux_gaming/comments/57clur/cant_run_steam_on_ubuntu_1610/
It's for Mesa on Ubuntu 16.10, but can be helpful with 16.04 too.
In short, use steam from Ubuntu repos and tweak steam launcher script to remove broken libs.

Borderlands TPS (don't know for Borderlands 2) seems to work this way.
Could also be a problem on 16.04 because of an older mesa version.

run Steam from the terminal like this:
LIBGL_DEBUG=verbose steam
then see if it outputs some library issue or so..

Anyway you should be able to run steam just by bypassing the libstdc++.so.6 library

The basic problem is not the open-source drivers, but that Valve is shipping an outdated library with the client. Usually people delete those files or bypass them, like you did. You can find plenty of information on this problem.
Whether your Borderlands problem is related, I don't know. Maybe it has a totally different reason and of course, a different solution.

Borderlands 2 does not launch from steam for me either. However, it should launch from the terminal ~/.steam/steamapps/common/Borderlands\ 2/Borderlands2 after doing echo 49520 > ~/.steam/steamapps/common/Borderlands\ 2/steam_appid.txt

Off-topic:
Since you are using open source drivers, I suggest running it in wine with gallium nine. Much better performance.

Thanks for the suggestions. I found a launch option on reddit that worked to fix borderlands 2 and borderlands TPS SSL_CERT_DIR="/etc/ssl/certs" LD_PRELOAD='./libcxxrt.so:/usr/$LIB/libstdc++.so.6' %command%. I am using the steam launch command that was recommended on OMGUbuntu. @dderp I understand your point about performance but it is more than playable for me and I don't want steam to pop up a survey thinking I'm in windows. The one bad point about this launch option is it disables the steam overlay so no FPS counter.