First of all, it should be noted that this text says nothing regarding auricular confession or priestly absolution. Rather, sinners were simply to bring their guilt offerings (which were temporary coverings for sin) for the priest to make atonement. The priests managed the particulars of the Mosaic system. They supervised faithfulness to the Law. The priests presented gifts and animal sacrifices according to God's commandments.
In offering up sacrifices for the sins of people, priests were to announce the means by which God chose for forgiveness. They were only doing as God instructed them. This is similar to how Christians under the New Covenant clearly communicate the gospel and proclaim the way that God has chosen to offer forgiveness for our sins (1 Peter 2:5-9). The sacrificial system of the Old Covenant pointed to the once for all sacrifice of Jesus Christ. Besides, it is not as though Roman Catholics bring bloody animal sacrifices each time that they go to the confessional.
Even if the Jews were supposed to confess sins to their priests (something that is not indicated by this text, nor the rest of the Old Testament), the point remains that Christ abrogated the Levitical priesthood. His sacrifice has done away with the Law. We have direct access to God through the shed blood of Jesus Christ (Hebrews 10:19-22). An ordained ministerial priesthood has been cancelled out by His everlasting High Priesthood. We must place our trust in His work alone for salvation. While the confession of sin is very much a biblical concept, there is no basis for receiving the forgiveness of God by confessing sins to a mortal man.