No problem. There is no doubt that gentile Christians, which Justin Martyr was, had already begun to distance themselves from Jewish converts as soon as 100 years after the death of Christ. Martyr spent most of his life in Rome where false Gods were rampant. Perhaps worshipping on Sunday served two purposes: It didn't look so suspicious since there was weekly feast to the Sun god on that day...and it also served to make them appear less "Jewish". Either way it did seem to be a departure from from scripture.
But I think the authors intent wasn't to prove that Constantine was the first person to come up with the concept of Sunday worship, but was the person who made it official for the Roman church, which ultimately became the Roman Catholic church and her protestent sisters.
Christians to this day continue to argue over these things, but as he pointed out in Romans, we should not do so.