As you already guessed yourself, RAW this would be a GM fiat.
If I apply some kind of logic (and a bit of humor) in this magic item concept, the beard will grow as thick as the thickest dwarven beard in the multiverse because the Belt of Dwarvenkind should never betray its people giving a non-dwarf the thickest beard there is; Moradin wouldn't approve that.
In the case of a Dwarf user, the belt would elevate his beard to the glorious thickness of Moradin's beard; a great honor for every dwarf.