Nah, you don't buy securities, you can only long / short them.
Yes, you go long or short, but TorBroker trades the securities in the real world, which is a traceable activity not amenable to anonymity.
An excerpt from the original post:
4. Pick a security to long or short. At the next market opening, we will mirror your position on the real market.
5. Exit the position. At the next market opening, we will exit our position on the real market and credit your account with the resulting gains or losses.