Three New Year's Babies, One Family: Father, Son and Grandson Share Jan. 1 Birthday

You're of course right that there are a lot of families where people share birthdays. There are so many instances, that if this had simply been about the baby and his father, just the baby and his grandfather, or the baby and any other family member, this article wouldn't likely exist. However, the whole father, son, grandson thing stands out a little more than those instances, likely moreso because of it happening specifically on January 1st. That still isn't likely unique to them, but is apparently considered to be interesting enough to warrant this.