How does VPN overcome port block?

Background:

A few days back I wanted to play AOE2 over internet. For that I used Voobly application for finding the users and launching the game. But problem was that since my local ISP had blocked port 16000, I was unable to play. I asked the local ISP to forward the port 16000 and they didn't know what did that mean.

After that I installed Hideme VPN application and it somehow did the port forwarding and I was able to play.

Question:

How does the VPN overcome the port blocking restriction? Isn't all the traffic still go through my router, so then how did that happen?

Note: I first asked this at Network Engineering , they told me to move it here.