The additional checksum will allow verification of the data by the application software.
The transport layer, in this case the CANbus, will apply the checksum in hardware, so there is no check that the software that sent the signal has done any verification unless the additional checksum is added within the 8 bytes.
Also the 8 bytes, or some of the 8 bytes, could end up being translated into another CAN frame, or even some other transport mechanism, such as Flexray. In that case the CANbus checksum would only protect one transmission and not a second one. However, the 4 bit checksum within the 8 bytes would give end-to-end verification and detect glitches in the translation software, as well as in the transmission hardware.