Chunks of the password (of equal size, see the code) were stored in multiple chunk servers. From crashing the program or reading the code, it could be determined there were four chunk servers, so each hosted three characters of the password.

Using a port-counting vulnerability (sending multiple identical requests, and rejecting guesses where the difference in response port #s was too low: 2 for first chunk, 3 for second chunk, etc.) it was possible to brute force each chunk server in sequence.

Thus, the problem space was 4*10^3 rather than 10^12.

You only need 1 call per possible number for each chunk, yes. But since the numbers are random between 0 to 999, that averages to 500 requests per chunk. Additionally, you don't have to do any kind of port checking for the last chunk, so that saves on any overhead you might have for the port checks. Based on this I'd say there's (3x 500 requests + 20% overhead) + 500 requests for the final block. That's 2300 requests on average.