First of all, YES you can play co-op with steam remote play. I am still not sure if this will be a real feature of the game, I did it mainly because I wanted to play with my kids now we are playing different co-op games (we even played the dome keeper playtest and we loved it), so I just started with adding a new ship and controller, it worked and from there it scaled until now you can play all the game with friends. Still deciding if announce it as a feature or just keep it hidden/optional (not sure if I can/should maintain it in the future). Anyways, here is the list of changes.
0.7.11 - Local Co-op Fixes
* Added: support for continue game when playing multiplayer.
* Added: different ships and ui icons for each play.
* Fixed: keep each ship progress after travel when playing local multiplayer (can't continue co-op savegame yet)
* Fixed: removed camera audio listener when playing local multiplayer.
* Fixed: in co-op friendly ships were not respawning in the location of the ship debris if pushed (note: can push debris to other locations and then respawn friends).
* Fixed: repair drone wasn't repairing anything.
* Fixed: minerals were multiplied when playing local co-op and jumping to next asteroid.
* Fixed: anomalies attacking ship debris in co-op.
* Fixed: "single" multiplayer game was overriding singleplayer savegame.
* Fixed: blueprints now apply correctly to all players when picking them in local co-op.
0.7.10 - Local Co-op
* Added: Local co-op support to play with friends and family, but for now is a WIP, not done, and might not even be part of the game in the future but I wanted to play the game with my kids xD
* Changed: increased scout drone vision range and renamed to Mineral Scout to make his main task more clear.
* Changed: increased hp for all drones.
* Changed: increased repair drone search distance and fixed to consider all damaged allies.
* Changed: UI for ship health moved to the center of the screen at the bottom.
* Changed: trying a new input configuration for gamepad dpad ui navigation to see if it improves some gamepads ui nav issues (xbox wireless controller, I am looking at you right now).
* Changed: important items now reveal vision once discovered, also emit particles and in some cases have some additional sfx in order to help finding them.
* Changed: enemies can't attack the drones factory now.
* Known issue: when playing coop only first player progress is kept after travel to next asteroid
Here I am playing with a friend with remote play, it just works (I love you valve):