It looks like Steam is getting a new feature offering automatic online support for local multiplayer games. Dubbed 'Remote Play Together', the feature was announced on the Steamworks website, which only devs have access to, though a couple have already shared the information publicly.
According to the announcement, Remote Play Together will enter Steam beta soon, and will allow "two or more players to enjoy local multiplayer games over the internet, together."
The announcement goes on: "All local multiplayer, local co-op and split-screen games will be automatically included in the Remote Play Together beta, which we plan to launch the week of October 21."
Nvidia used to have similar functionality in its GeForce Experience app, and low-latency game streaming services like Parsec have supported it for a while. As the name implies, it basically uses remote play functionality to simulate the experience of playing together in a room (short of having the other players actually in the room).