The most likely reason you are presented with this error is that CS:GO is still running on your computer. CS:GO must be started from the ESEA Client to play on ESEA servers. This is due to the way the ESEA Client secures the game to protect against cheating.
To make completely sure CS:GO is not running before you attempt to launch it with ESEA, navigate to your Task Manager (Ctrl+Shift+ESC) and end the CS:GO process as displayed below.
Note: Sometimes, "Process Lasso" and similar tools can cause Error #107. Try uninstalling that software, followed by restarting your PC, and see if the issue persists. If the issue does persist, please reach out to us here for assistance.