Would sexual addiction and the severity of the adultery be considered a crime in Washington State? Example: Children out of Wedlock, Multiple affairs

Adultery is NOT a crime in any developed country of the civilised world.

There are a few US states where it is still listed as a crime, but it is not enforced. So no, there will be no criminal issues because of this, Adultery is handled in divorce court. Children out of wedlock are merely children, who he will pay child support for.

If you are the wife, the best thing is to just file for divorce and move on, there will be no criminal issues from this The US has stopped enforcing "bedroom" laws years ago.

To answer the question, no. I don't see it here in the Washington Criminal Code. One would expect to find something in Chapter 9A.64; it's not there.