The procedure for requesting an eID or Kids-ID (if your child is 6 years old or over) changed on June 2021. Since then, the application for an identity card must be done in person (6 years and up) with an appointment via e-Appointment.
The Embassy of Belgium in Tokyo only issues electronic identity cards to registered Belgians:
Onderscheid en karakteristieken identiteitskaart – paspoort - verblijfsvergunning
Every Belgian citizen registered at an Embassy or consulate and who is aged 15+ must have an identity card. For children under 15 years of age (0-12 Kids-ID, 12-15 eID), this is not compulsory. The newest generation of Belgian identity cards has an electronic chip (hence the name “eID”) containing the data of the person, (the address is not mentioned, only "Tokyo, Japan"). The holder of an eID always has the right to verify these data.