‘In this was the love of God manifested in us, that God has sent his only unique Son into the world that we might live through him.'
God's love as in mind in this passage is a love revealed in sending ‘His only unique Son', (in other words the only One of the same essence and being as Himself. This is using human terminology to depict a divine truth), into the world that we might live through Him. He sent Him in His great love, so that those who would truly respond to Him might have life. And the life we receive is His life, given to us, so that it reproduces His own righteousness and love. It will thus be revealed in love of those who are His.