In general, there are two parts of this.
The "remote and event-based" part: Service used remotely over network needs certain set of skills: to be able to accept (multiple) connections, read requests, process, reply, speak at least basic TCP/HTTP, handle dead connections, and if it's more than small private LAN, it needs to be robust (think DoS) and maybe also perform some kind of authentication.
If your script is willing to take care of all of this, then it's ready to open its own port and listen. I'm not sure if web.py provides all of these facilities.
Then there's the other part, "daemonization", when you want to run the server unattended: running at boot, running under the right user, not blocking your parent (ssh, init script or whatever), not having ttys open but maybe logging somewhere...
Servers like nginx and Apache are built for this, and provide interfaces like mod_python or WSGI, so that much simpler applications can give up as much of the above as possible.
So the answer would be: yes, you still need Nginx or the likes, unless:
you can implement it yourself in Python,
or you are using the script on localhost only and are willing to take some risks of instability.
Then probably you can do on your own.