Nobody is saying that the computational model necessitates an afterlife, only that it would make it possible.
Define 'possible'. Technically it is 'possible' to create an Afterlife in
this universe, with a sufficiently advanced technology. The question is not whether it may be 'possible', but whether it is
actually occurring.
The problem with a computational model is that in order for a person's mind to exist intact beyond death, it must be copied and stored somewhere
before death. Why? Because the mind has probably already been destroyed (by oxygen starvation, trauma or disease) when the body finally dies.
But when does the program decide to back up your mind so that it can be regenerated later? Our minds are constantly changing as we experience life. Imagine that you have a massive stroke and a large part of your brain dies. Your mind has now been markedly diminished, but part of it still exists. Later, when you die, does the computer use a backup copy made before you suffered the stroke, or after? If before then it's not really 'you', but an earlier version. If after, then it's not a fully intact 'you', but a damaged version. In neither case is true Life After Death achieved.
As an analogy, imagine you are typing a story into your computer. To ensure that you don't lose your work, you make a backup copy every few pages. Unfortunately, you were just about to back up the last 3 pages when a power glitch corrupts the document. What do you do? Try to fix up the mess of corrupted text, or reload from the backup and try to remember what you typed into those last 3 pages? Either way, you don't have a good copy of your document!
Regarding the part about existing separately from this simulation. That too is entirely possible. Just add another universe ( call it universe_2.exe ) and take our data sets that have been stored in memory and insert them into it. Presto ... we've died in one universe and are alive in another!
With a fully re-entrant program you don't even need another executable, just run it again with other copy of the data sets. But when you run the program on the copied data sets, it executes exactly the same instructions so the mind/person still dies!
In order to achieve true Life After Death, the program must have some way of moving a person's mind to a different environment (another body, an ethereal form etc.), otherwise the mind is not really surviving death, but is just a re-run, doomed to repeat exactly the same death sequence.
If there existed a record of our entire existence, then we could be resurrected with complete memories and fully intact bodies. In every meaningful way this would amount to life after death.
Or would it simply be a
recording of our existence, and the resurrected bodies merely
copies of our own? Let's say I had a machine that could duplicate the position and momentum of every particle in your body, accurately enough that it could create a functionally identical copy of your mind. Would you be happy if I was to kill you now, since your mind will continue to exist in the other body? Or is the clone an imposter?