Unbelievable! The artifacts perfectly fits one of the slots in the platform's pedestal. How did I not notice that right away? I really am a dipstick.
So if this key, such as it is, was acquired by activating one of the obelisks, then it follows that the other two keys can be obtained by activating the other two obelisks. Then, with all three keys, maybe this platform will lead to whatever is controlling the Island's ecosystem.
If the other obelisks work the way that the first one did, that means I have to find a whole mess of artifacts first, and I don't think I can do that alone...