On another account, in 2016, regarding the DMM Kamihime, the same "enter you serial number" thing existed for some time. It seemed like it was connected to a special receipt regarding a virtual character's upcoming artwork. Maybe at anime expo, you can buy things from Nutaku's booth, and register a serial code from there. Who knows, I won't be in LA, I live in Greece -.-

Most probably though, these serial numbers are exclusive to one per person and regard either exclusive Kamihime, or important ones (for example the unintroduced Trap element, who knows)

If anyone goes to the convention and happens to drop by or finds info, I'd appreciate some sharing of knowledge :/