Judging from the error output you get the error is not with the system install of mapnik, but with the node dependency windshaft:
The source of the failing file:
has the following line:
, mapnik = require('mapnik')
Since this require fails for you ...
The local system browser knows about your domain just because you've added an /etc/hosts entry pointing domain to your localhost.
I see two ways for you to see your cartodb from a remote network:
a) accessing your computer using it's public IP, like this: http://public_ip:3000
b) having access to your DNS server and inserting Address records for your ...
The mapnik version error was a bug in the testsuite, which wasn't expecting anyone to change mapnik_version in the test.js configuration file.
Thanks for spotting it, now fixed :)