I thought I had allowed connections to http-alt (8080) using ufw. My reasoning for thinking this is because:
gerrit2@localhost:~$ sudo ufw status
Status: active
To Action From
-- ------ ----
22 ALLOW Anywhere
80/tcp ALLOW Anywhere
8080/tcp ALLOW Anywhere
22 (v6) ALLOW Anywhere (v6)
80/tcp (v6) ALLOW Anywhere (v6)
8080/tcp (v6) ALLOW Anywhere (v6)
and
Chain INPUT (policy DROP)
target prot opt source destination
ufw-before-logging-input all -- anywhere anywhere
ufw-before-input all -- anywhere anywhere
ufw-after-input all -- anywhere anywhere
ufw-after-logging-input all -- anywhere anywhere
ufw-reject-input all -- anywhere anywhere
ufw-track-input all -- anywhere anywhere
...
Chain ufw-before-input (1 references)
target prot opt source destination
ACCEPT all -- anywhere anywhere
ACCEPT all -- anywhere anywhere ctstate RELATED,ESTABLISHED
ufw-logging-deny all -- anywhere anywhere ctstate INVALID
DROP all -- anywhere anywhere ctstate INVALID
ACCEPT icmp -- anywhere anywhere icmp destination-unreachable
ACCEPT icmp -- anywhere anywhere icmp source-quench
ACCEPT icmp -- anywhere anywhere icmp time-exceeded
ACCEPT icmp -- anywhere anywhere icmp parameter-problem
ACCEPT icmp -- anywhere anywhere icmp echo-request
ACCEPT udp -- anywhere anywhere udp spt:bootps dpt:bootpc
ufw-not-local all -- anywhere anywhere
ACCEPT udp -- anywhere 224.0.0.251 udp dpt:mdns
ACCEPT udp -- anywhere 239.255.255.250 udp dpt:1900
ufw-user-input all -- anywhere anywhere
...
Chain ufw-user-input (1 references)
target prot opt source destination
ACCEPT tcp -- anywhere anywhere tcp dpt:ssh
ACCEPT udp -- anywhere anywhere udp dpt:ssh
ACCEPT tcp -- anywhere anywhere tcp dpt:http
ACCEPT tcp -- anywhere anywhere tcp dpt:http-alt
However, when I go to see if that port is open with nmap I get the following:
[mehoggan@localhost ~]$ nmap -p 8080 matthewh.me
Starting Nmap 6.45 ( http://nmap.org ) at 2014-07-07 20:00 PDT
Nmap scan report for matthewh.me (50.116.18.212)
Host is up (0.050s latency).
rDNS record for 50.116.18.212: li418-212.members.linode.com
PORT STATE SERVICE
8080/tcp closed http-proxy
What do I need to do to open that port up to the outside world using Ubuntu's 14.04 ufw?
You did open your firewall correctly. In order to "open" the port, you need to actually have a service running that listens on port 8080.