Only Those In The Direct Line
To be specific, the proclamation said, “The grandchildren of the sons of any such Sovereign in the direct male line (save only the eldest living son of the eldest son of the Prince of Wales) shall have and enjoy in all occasions the style and title enjoyed by the children of Dukes of these Our Realms.” In essence, you are not considered a prince unless you are a part of the direct line to the throne.
It Is Not Just For Male Heirs
The “male” bit of this ruling has changed a bit over the years. Prior to the birth of Prince George, the government of the United Kingdom took on “absolute primogeniture.” This means that the first-born child of the heir can ascend the throne no matter the gender. An older girl is always going to be ahead in line of a younger boy. This must have been done in the name of gender equality.