In gleaning what these men have said, it is the way we live that reveals the children of God. John is especially clear that the accent is on doing. Now in this context what is righteousness?
We may be able to give a legal definition from Psalm 119:172: All your commandments are righteousness. But that is a bare-bones, legal definition of what righteousness is. In the context, it is to love our brother. To not do anything is a form of hatred. It is almost equated with murder. John says what we have to do is to reach out and really help the person.
There is something we can do. We might not be able to help the person physically because we are simply unable to do it - we are not where they are, we have not the mind (the technical expertise), or the resources in terms of finances, or whatever to actually do something that way physically - but the very least we can do is pray for the person. That is doing something, is it not? That is expressing your concern for the person to God. Surely we can all do something like that. That is an active step toward doing righteousness, a very important one.
So we can have fine words, fine thoughts, fine feelings, but none of those things will ever take the place of deeds. God's emphasis is always on action. Christ laid down His life for us.
They were ignorant of God's righteousness. Righteousness simply means right doing; rectitude. According to Psalm 119:172, righteousness is defined as the commandments of God. That is right doing! So we see here that, by definition, these people did not know of God's right doing - God's right way, God's right method, God's commandments. We see that confirmed in Mark 7, where Jesus said:
Brethren, it says in Psalm 119:172 that ALL of God's commandments are righteousness. Understanding is the result of doing the commands of God. When we stop doing, we begin to lose the understanding. It is not something that will happen quickly. It will not happen overnight, or in the blink of the eye. But, in the biblical milieu there, You use it, or you lose it.