Everyone who controls private keys to a set of stakes that need to be investigated (excluding those from Nxt AE I think) launches NEM wallet and leave it open. At some moment (triggered by Bitcoin block N, data can be gotten from Blockchain.Info easily) all the wallets start solving cryptographical puzzles depending on Bitcoin block hash and NEM account id. In 15 minutes these puzzles are sent to a server controlled by NEM devs and the hash of received puzzles is published and copied by a lot of people who have to wait these 15 minutes.

After that we can make a good assessment how many computers "controlled" by a particular NEM stake and we can verify the puzzles because their hash is publicly known. Someone owning 100 stakes have to find 100 computers.