Understanding WannaCrypt's hybrid encryption scheme
The server will never release Spriv, it protects all ransomed clients. 
Assuming the server wants to allow a given client to decrypt it's file the server will use Spriv to decrypt Cpriv and send that to the client. 
With Cpriv only the paying client/victim can decrypt the various symmetric keys $K_f$ and use them to decrypt his files. 

It is worth to discuss a simpler solution not mentioned in the video where all files have the same symmetric key (and different nonce/IV), and the symmetric key is encrypted directly with Spub. Such a setup will have the single client private key available on the client until encryption is done, This is problematic for the ransomware, as they want the client key to be gone from the client asap making it impossible to stop the process mid way and capture the client key. By making a separate key per file, and encrypting that with a client public key with private key long gone this is averted. Even if you catch the process half way through you can't undue what is done without interacting with the holder of Spriv(paying the ransom). 

Think of all the good that could be accomplished if the clever people writing malware actually directed their skills in a positive direction?