Two possibilities come to mind:
1) After the declaration of forgiveness, the rest of the paragraph addresses God directly and asks Him, among other related things, to erase one's sins. Perhaps the declaration of forgiveness is essentially the introduction to this request, as if to say, "God, just as I forgive all who have acted against me, please forgive me for having acted against you".
2) The origin for this custom may be the Gemara Megilla 28a, which recounts Mar Zutra's declaration of forgiveness every night. According to the Bach's version of the text, it reads "God should forgive all who have wronged me". It was a plea to God to forgive them, in addition to being implicitly a declaration of his own forgiveness. Perhaps that is the implicit meaning of the words 'ribono shel olam' here.