I think in such a scenario intelligent design of lifeforms would be treated in exactly the same way that we treat intelligent design of mechanisms. There's no need to introduce any kind of new thinking. It would simply be a design problem as faced by engineers all over the world. A somewhat more complex design problem, to be sure. They'd probably have pretty sophisticated CADLife programs.
That could be a possibility. Biology and engineering become one in the same.
Individuals would want to fix problems with limited lifespan. Socieities might then suffer from the problem of individuals with unlimited lifespam.
The effects of immortality on society sounds like an interesting topic to devote another thread to. But, I am sure most of them will get over their suffering by simply insulting each other.
More seriously, I think the survival factors of such a race would be completely different, if the genetic-like system they employ is completely different. In my view, I suspect something closely akin to memes would be the new, dominant replicator. And, that means the problem of the individual living forever would be irrelevant. All they strive for is to spread their memes.
Though, the "memes" themselves would probably be in a different form, more like a weird meme/computer code/gene thing, of some sort.
But, that's just my wild and crazy idea.
Even if the aliens had a genetic structure, and immortality was possible, perhaps "fill out space" becomes the next goal: Just keep traveling to planets, and filling them up with entities. If there is no more room on nearby planets, you stop reproducing. But, that's okay, you and your existing progeny will still around for looooooooooooooooong time.
Perhaps the limited lifespan problem would appear intractable leading to a quest for the technology of the designers - and then we have the plot of blade runner/do andriods dream of electric sheep.
In a sense, that has already happened in my revised scenario. The aliens would be the replicant/android things.