The article comments mention that you need to have the Bitcoin wallet address to use the tool to decrypt the files. Either they found some relationship between the wallet and the secret used for the encryption, or they actually compromised the servers and have a true mapping between every wallet address and the key subsequently used for that encryption.

The article says they were given the keys by the police.

The article states they "...obtained a database from a CoinVault command & control server (containing IVs, Keys and private Bitcoin wallets)."

Reading between the lines, the police located the server, served a subpoena to the hosting company, and took possession of the server. They then turned it over to Kaspersky who created the site based on the keys on that server.

The screen dumps are just showing how they figured out the decryption routine - the private key alone doesn't do you much good if you don't know the algorithm used.