That's not true. Volcanic eruptions are not "computational engines running algorithms." Nor is the Sun. You can simulate something as predictable as the orbit of the Moon around the Earth, but that doesn't mean that its every movement around this planet is dictated by a computational engine running an algorithm. Simulation should never be confused with reality.
In contrast to your misinformed claim, "programming" is useful because it differentiates intelligent intervention from random mutations or events.
"The behavior of DNA is as intelligent as the behavior of every other chemical process that is occuring."
Nonsense. DNA has an ordered structure that enables repeatable transmission of high-value data. Thus, DNA's predictable replication of various life forms is VASTLY more "intelligent" than the chemical breakdown of rocks that are naturally pounded with rain and rivers because the DNA predictably conveys information, whereas the stream does not.
You have a pedestrian definition of "computation" that is not useful in a rigorous discussion. If the discussion is to have meaning, precise and rigorous definitions need to be used.