I'll go a step further.
The argument in the OP seems to rely on the part-syllogism: There cannot be values without life; therefore life is valuable.
Now perhaps most folk would agree that there cannot be values without life, and think life is valuable, and yet agree that the second does not follow from the first.
There is a gap between the "is" of "There cannot be values without life" and the "ought" of "Life is valuable.
So let's try to put the argument, as given together, and see where the problem lies. Most obviously, the interpretation above is not a syllogism, since it has only one premise. So is there a second premise, and if so, what is it?
What was called a "formal" version remains a bit unclear, but seems to be found in the following lines:
1. Without life, there is no subject to generate or interpret value.
2. Life persists by resisting entropy through structure, order, and adaptation, and “Good” can be structurally defined as that which reinforces this persistence.
3. For life to continue, it must operate as if life is good.
It's hard to see how (3) follows from (1) and (2) in any formal way. The idea seems to be that since life does persist, it ought to persist. But that does not follow.
In addition, there remains the obvious question:
why ought life continue? Perhaps what
ought happen is that life ought be deleted, maybe in order to remove all suffering. Again, I am not advocating this, but pointing out the logical gap in the argument.
Some folk will read this and not see that my counter isn't about whether life is valuable or whether life ought continue, but about the lack of validity in the argument. We cannot move from the observation that there is life, to the conclusion that life is valuable, without introducing an evaluation. We cannot move form that A exists, to that A is valuable; at least not without introducing a second premise - but this premise must introduce the value of A. We can't get form an "ought" to an "is", at least nto int he way suggested in this thread.