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https://en.wikipedia.org/wiki/Spawn_installation - I was going to say that StarCraft 1 had this, but it turns out it was a whole category of games!

Steam remote play?

that isn't quite the same, ds download play sent a small multiplayer-only to the guest device, independent of the host device. Remote play merely streams your whole session over.

The only thing close for the PC market I can think of is It Takes Two and its "Friends Pass"

Operation Tango is another example of a free install for player 2.

The PSP had game sharing, basically the same: send a small multiplayer/demo copy.

Some Gameboy Advance games had it, too.

Advance Wars was one of them.

Huh, I was just thinking of that myself, but I didn't know Steam already had this feature. It's a great idea and something I'd like to make more use of.