Yes, people with double citizenship are eligible for the Japan Rail Pass.
For this entry into Japan, they must enter using their non-Japanese passport in order to get the “temporary visitor” visa. This means that children of Japanese nationals with double citizenship must enter under the nationality of the non-Japanese country, different from their parents who enter under their Japanese citizenship.
Please note that a person with dual citizenship who has entered Japan using their Japanese passport will not be able to exchange their voucher by showing their unstamped non-Japanese passport.
The most important thing is to make sure you get a “temporary visitor” visa.