OK, I think I got it (and an easier way than messing with NAT on Linux

)
I used Chrome, but any other browser is probably fine too, with a similar procedure. The idea is to trick the webpage into serving you a HTML5 version of the video, instead of the flash version. First you have to trick them into thinking you don't have flash, and then you have to trick them into thinking you can't install it either.
Step 1. Disable Flash.
In chrome type "chrome://plugins" (without double-quotes) into search bar
Click "disable" next to Adobe Flash Player
Try a TG4 link, like:
http://www.tg4.tv/play.php?pid=44253652 ... acht%20TG4You should see a message urging you to install flash on your computer instead of the player - that's good. If you still get the video it means you have to disable flash harder

Step 2. Trick it into thinking you can't get flash either.
Get a plugin which allows you to switch the user-agent of your browser, like
https://chrome.google.com/webstore/deta ... pkjnoahfmgSet it up so your browser claims it is one of the mobile devices. Windows 8 Phone worked for me. You should get the video again if successful.
Click the "play" button on the player, once it starts playing right-click the video and and option "save the video as" should be present in the menu.