The appeal to incredulity fallacy is pretty much just the assertion that something can't be true because it seems too fantastic to the debater--that is, he doesn't personally believe it. It's a moronic argument on its face, for obvious reasons, but it is popular with the undereducated. What you're talking about RE: biochemical life and intelligent design is more in the line of a huge leap of logic. They're stating that biochemistry is necessary for life and is therefore evidence of design, without actually proving anything of the sort.
I'm not sure if there's a specific name for this fallacy, but I would characterize it as the assumption that certain outcomes (e.g. "life as we know it") are essentially more favorable than others and the universe intended for them to come about. Human life is the goal at the end of natural history and was always so, and given that human life is a wildly improbable condition (millions of worlds, only one with us) it must have been the product of design. In reality we know that life as we know it is just the current state of an ongoing physical process and is not really special in any existential sense. The universe and its physical laws do not favor or disfavor human life any more than they favor the rings of Saturn or Quasars--they are just things that happen in the presence of specific conditions. In a way I guess you could say that it is an implicit appeal to incredulity, because the debater refuses to recognize that.
So your proposed argument is taking something that is known to exist and, with no support whatsoever, asserting that it is proof of design. I would call it the "just make shit up" fallacy. You could as well say that anything in nature was proof of design.
Direct analogy is actually a good way to demonstrate the logical fallacy here:
The physical process of boiling is proof of design because it allows me to make hardboiled eggs.
It's easy to see the leap of logic, here. Water that has been heated to 100 degrees Celsius and is undergoing phase transition to gas doesn't give a shit about hardboiled eggs, any more than biochemistry cares about producing life. It's just a natural process that can produce that result, given the right conditions.