Is it valid for Fatwa No. 8065 to suffice with urging the spouses to repent after their confession of adultery, without mentioning the carrying out of the prescribed punishment upon them?

The woman's confession mentioned in the question was not made before the ruler. Unless the matter reaches him or his deputy, the hadd punishment is not obligatory. What is required from the sinner and from whoever becomes aware of the sin is to conceal it and encourage repentance, because the implementation of hudud punishments is the exclusive prerogative of the ruler or the sovereign.