Media mode option is only existed on as-2 and as-3 series. as-6 series does not have this option (it should imply that it always enable media mode).
You need to install ASUSTOR Portal (from App Central) to see video output through HDMI. However, from your descriptions, you encountered problems to connect to asustor server. You can try to setup DNS to google DNS server (8.8.8.8). You can find the setting in ADM web page -> Settings -> Network -> DNS server.
