Firstly, that statement doesn't mean "don't bring a computer"; it means " you don't need to bring a computer". Many people going to their first key signing party are likely to assume that, since the keys are intended for use on computers, they will need to bring a computer containing their keys, signatures, or encryption software. What actually happens is that the verification of the keys takes place using key fingerprints without any computers and is entered into an online database after the event from participants' own computers at home.
Secondly, as a computer is not used at the key signing party, it is generally discouraged to take a computer to a key signing party. Having unnecessary computers at an event of that kind is a large security risk, as a malicious participant could use another participant's computer to sign his own key with the other participant's signature, or he could even steal other people's private keys or distribute malware. In short, computers are not necessary at key signing parties and having them present would introduce all the security risks that computers inherently bring with them, which is never a good idea when those computers are likely to contain private encryption keys, so most key signing parties prefer participants to write public key fingerprints on paper and keep their private keys safely at home.