There is a property in the DataModel called CreatorId that tells scripts who owns a game, however, the property has been broken in Roblox Studio since Accurate Play Solo rolled out, by which I mean it’s always set to 0 on the client side.
It works properly in a live server, and it did work fine in Classic Play Solo.
To see the bug:
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Open a game from the cloud in Roblox Studio.
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Play Solo.
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Run this in the command bar on both client and server:
print(game.CreatorId)