I'm really intrigued by how the data transfer works. In the video linked in the article, you can see them triggering the configuration panel of the chip by doing SYS54301, which effectively amounts to a jump instruction to address 0xD41D. The SID addresses range from 0xD400 to 0xD41F, with these addresses only being assigned to registers up to address 0xD41C. So, this is a jump to the first non-register address, with 3 bytes in the SID's address space that are normally being unused. Enough for a jump instruction itself. You could then technically have the Pico dispense the programme code in a tight loop using those 32 bytes as a tiny memory window into the code, 32 bytes at a time, each of them ending with a jump instruction to the start.

But can it play Doom?

Looks very interesting. It had me at Boulder Dash.