By the time content plays, it is already sitting on the device. The screen draws from that local copy, not from a live connection to the internet. The network’s job was to deliver the file; once delivered, it steps out of the way.
This is what keeps playback smooth. A slow or busy connection does not stutter a video, because it plays from the file already on the device rather than coming down the wire as it goes. The file is right there.
Live content is the exception. A live video stream, or a web page pulling fresh data, is fetched as it plays by its very nature, so it leans on the network the whole time it is on screen. That is the trade that comes with dynamic content: it stays current because it keeps reaching out, where a downloaded file stays smooth because it does not have to.
That local copy is also what keeps a screen running when the connection drops entirely. A screen that loses the internet keeps playing the content and schedule it already has, and the audience sees no difference. When the connection returns, the screen catches up: anything you changed while it was offline syncs across, and the screen moves on as if nothing happened.
The one limit is content it never managed to download. A file added while a screen was offline cannot play until the screen reconnects and fetches it. Delivery is automatic, but it still needs a moment of connection to happen.