Now, let us say we stumble across a watch lying on a beach. It is precise, it is well structured, and yet, it's extremely simple. There is not a great deal of noise in it, and the amount of information required to recreate it exactly is large, but not so large as a pile of rocks.
When SETI searches the skies for signals, they don't search for complicated signals. If they were looking for complexity, they'd have been done a long time ago. The skies are full of complicated radio signals. What SETI is searching for is an artificial signal- the clearest sign of artificiality? A sine wave. Extremely simple. And that makes it clearly artificial.
So simplicity is the sign of a creator, not complexity. It is a reduction in entropy that signals that a creator was involved.
The watchmaker argument fails, but that's because it was borne out of a time where we thought the movements of the planets were as precise as a well made clock. Before we could measure just how damn noisy the Universe really is. Complexity in nature is simply a consequence of nature's behavior, not a sign of intelligence. Simplicity is a sign of intelligence.