The goal would not be to construct the same mind or memories, it would likely be to convey some amount of meaning. Here's an excerpt from the essay which imagines a scenario where we exist in such a simulation:

>an entire history of people before us [...] decided their carefully spun web of love was worth living again. Maybe we don’t share their memories, but they looked like us, loved like us. We are their memorial. They decided – through their love, heartache, and scientific toil – that they would do anything to say “I love you” in a spectacular gesture that transcends universes.