Instead of having to tell a settler to equip, it will automatically be equipped as soon as it's on their inventory. Most settlers and humanoid companions, apart from Hancock and Nick Valentine, will also equip it if given to them.
It is listed as a miscellaneous item, as it cannot be equipped by the Sole Survivor (who already wears a Pip-Boy of their own), but it can be equipped by some NPCs, such as Clem. It is identical in appearance to a Pip-Boy 3000 Mark IV, the same model used by the Sole Survivor. The Vault 88 Pip-Boy is a miscellaneous item in the Fallout 4 add-on Vault-Tec Workshop.