Well,but why are the York Princesses styled "Princess" and the children of Princess Anne and Prince Edward aren´t?
They are also grandchildren of a Monarch and children of a (well, Princess Royal and) a Duke.
And they are also non-working Royals.
Bye Bine
The 1917 Letters Patent or rules on who is or who isn't an HRH Prince or Princess:
1. The children of the monarch - Charles, Anne, Andrew and Edward
2. The MALE LINE grandchildren of the monarch - William, Harry, Beatrice, Eugenie, Louise, James, Richard, Edward, Michael and Alexandra (Elizabeth herself was, like Beatrice, the elder daughter of the second son and Margaret was born in Eugenie's position of the younger daughter of the second son - the only other one born with HRH since 1917 was Prince William of Gloucester who died in 1972. He was the elder son of the late Duke of Gloucester)
3. The spouses of the men - Camilla, Sophie, Kate, Birgitte, Katherine and Marie-Christine
4. The eldest son of the eldest son of the Prince of Wales - George
In 2012 The Queen modified these LPs to allow ALL of William's children to be HRH Prince/Princess.
In 1948 George VI also modified the 1917 LPs to allow ALL children of HRH The Princess Elizabeth, Duchess of Edinburgh to also have HRH - otherwise Charles would have been born as Lord Charles Mountbatten, Earl of Merionth and Anne as Lady Anne Mountbatten.
Anne's children, like Margaret's and Mary's before her, don't have titles because they are descended from a girl and not a boy and as a daughter of the monarch Anne's children don't get titles without the monarch of the day doing something which didn't happen so no titles for Peter or Zara. Margaret's children have titles because Margaret insisted on her husband being given a title and The Queen agreed so he became Lord Snowdon and the children Viscount Linley and Lady Sarah. Princess Margaret married a man with a title in his own right so her children were titled through their father.
Edward's situation is different. His children are not using HRH Prince/Princess titles because he requested that they not be so burdened in 1999 when he was getting married. At the end of the 1990s the public were not in the mood for more royal children to be born, unless they were Diana's descendants whereas when Andrew's children were born there was never any suggestion of them not having the styles they were entitled to by the 1917 LPs.