Has anyone got League of Legends working on Linux Mint 18? I'm using the "Wine" plugin "Play on Linux" and it crashes on startup everytime.
I think your PC doesn't support League of Legends .
In Linux some games doesn't work, You can try to check if your PC supports requirements.
If your PC has the requirements, you can install a virtual machine with Windows 7/8/10. If your PC has 4GB, put 2GB in Virtual machine, If your PC has 8GB, put 4GB in virtual machine etc.
You can install a virtual machine using this tutorial.
Try updating Wine. The latest version is 2.21-staging; also remember to set it in the Play on Linux configuration.