If the photographers did not stalk or harass Archie, and it was taken in a public place, or with a parent's permission, no law was broken. "Harassment, as outlined in the bill, means willful conduct that "seriously alarms, annoys, torments or terrorizes" the child." (from the link).
Also, the distribution of the photographs themselves is not illegal. From the link: "The bill also states that distribution of a child's image does not violate the law, but rather it is the act of creating it." (However, the U.K. does have it's own rules about publishing photos of minors.)
This is why you still see plenty of celebrity children's photographs in People magazine taken on the beach in Malibu or walking in Brentwood. The photos were taken in public, and the photographers did not stalk or harass the children.
There was a push to prohibit the photographing of minors in public places in committee, but it never made it to the Governor's desk (it's dicey under current Constitutional law). Jennifer Garner spent years lobbying for more protection, and her kids are still constantly papped.
The U.S. is not a great place for children's privacy.
(Also, although Harry and Meghan are always able to sue someone for harassment/stalking, the law cited is criminal law, not civil law. A D.A. would need to bring charges.)