We don't call home. Once you've downloaded the Docker container, the only outbound network traffic should be downloading the requested SWF once for Flash games on demand (or for actually playing the game online, in the case of e.g. Slither). You can cache the SWF if you don't want it to be downloaded each time you start a new container.

Other than SWF downloading or specific Internet-enabled environments, running offline should just work.