Yes, you do.
As per Dirac Research T&C, Dirac Live licensing is from a per unit basis. I.e. you can't purchase/use a license from one product and apply it to another one. For miniDSP to enable Dirac Live on the unit, we need to flash a unique Dirac Live license code inside the product. That code is unique to miniDSP and unique to that specific hardware (E.g. SHD). It unfortunately can't be shared with other products or other Dirac Live applications (E.g. Dirac Live processor) that you may have purchased in the past.