My nephew wants to play Roblox but we won't let him. However I have a Minecraft server that we can control and it's been running for longer than he's been alive. So with any luck we should be able to keep the map/game for a while longer.
But I also realized what you're saying when he was watching YouTube videos. When I was a kid I was watching cartoons and kids shows that now I can simply stream/download and rewatch. It's however going to be much more difficult to do with random videos on YouTube.