Both the RCM4200 and RCM4210 store and boot firmware from a 512KB parallel flash chip. The serial flash on both products holds data only.
On the RCM4200, the BIOS copies firmware from the parallel boot flash into a dedicated 512KB SRAM and executes from there with fewer wait states than it can when executing from the parallel flash. Because the firmware executes from SRAM, the Remote Program Update (RPU) library can overwrite the parallel boot flash. Note that on the RCM4200 there is a small failure window where power loss/reset during an update will leave the board in an unbootable ("bricked") state.
As a reduced cost product, the RCM4210 lacks the 512KB SRAM for execution (and reduces the 8MB serial data flash to 4MB). That's why it the RPU library doesn't support it.
Note that RPU supports the RCM5750, which also runs firmware from parallel flash. In that case, it uses a custom "mini loader" with memory mapping tricks to copy 12KB of code to RAM and then execute that code to erase and overwrite the parallel boot flash. But there are enough differences from the RCM4210 that it would require a significant engineering effort to adapt that code to the RCM4210.
If you require RPU functionality, you need to switch to the RCM4200 or another supported module (like the RCM4310 or RCM4320) that meets your other design requirements.