This is correct only for BSGS (Baby-Step-Giant-Step).
Using Pollard Rho method, the expected work is 3*2^80 group operations with almost zero memory requirements.
Note that unlike BSGS this method is probabilistic, and might fail with very low probability (on the order of 2^-160).
One can improve the algorithm using Distinguished Points, bringing the expected work down to 1.253*2^80 group operations, using both less memory and less group operations (on average) than BSGS.
Pollard Rho can't exploit the fact that the private key is in the range from 1 to 2^160 for example, because it is probabilistic. It would need always 2^128 steps. Only BSGS is suitable for this task.
If you try to retrieve #57 with Pollard Rho, you won't retrieve the private key in a few seconds or in a few years.
With "space search is 2^160" in this context we mean a 2^160 points subset in the space of the 2^256 points of the secp256k1 curve.