League Of Legends on Ubuntu lol Lancher.exe has encountered

I have never used Blackbox Linux, do you know if the Proprietary video drivers are installed or open source?
I would definitely try another game just to be sure...

• Open Arena
• 0A.D.
• Drox Operative

0A.D. is pretty harmless installation. I've never used Blackbox, but Ubuntu and Mint should have it in the software installer. Just search for 0A.D. and install it.
Otherwise, there are a bunch of other free games out there: Free Linux Games
Something 3D is preferred so we know if the video chip can handle it.
What video is running on your Acer3610?

Here are a bunch more free games on Desura: Free Games
Just install the Desura client and then create an account.
Login and search for one of those games on the list, then it will automatically install.

Diety is a good one and a small download

Blackbox must be using open-source drivers.
What video chip is your computer using: Intel, AMD, Nvidia?
I recommend searching online on how to install the proprietary drivers. Open source drivers rarely get the performance games need from the video chip.

I'm not sure what version of Blackbox you are using, but here is a Blog with some steps on how to install Intel drivers:
Install xserver-xorg-video-intel

Of course this is at your own risk. installing drivers can break things in Linux if they are not supported by your hardware or Linux distro.

I recommend going back to Ubuntu 12.04 and installing the automatic way.
My Chromebook Acer C710 has an Intel HD 2000 video chip and the drivers are automatically installed with ChrUbuntu.
But its pretty limited with gaming. I can't play a whole bunch of modern games.

I forgot to tell you that I did login to League of Legends and started a match.
Loading all of the Players takes a while, but I was in-game and actually played a bit. No problems. Not even a store crash.