i am trying to let my GameClient open a WebSocket Connection.
I found the libwebsockets package inside the Engine. But in the description of the Header file ther is written that its just a websocket server.
How else i can add websocket client functionality to my game ?
You can find a Websocket implementation for the libwebsocket library located in Engine/Source/ThirdParty/WebSockets.
Part of the private classes of that library are an implementation of a WebSocket in C++. You can copy that class to your project, rename it and use the websocket connection. This will limit your project to Windows and maybe HTML5.
At least I did something similar half a year ago with Unreal 4.8, but my projects are now outside of my reach. I hope this helps. Good luck!