I bought Humble Mozilla Bundle because I really like the idea that the game can run right in my browser, but I can't figure out how to load new cartridges into the game. Is this feature not implemented?

are you trying to submit a cartridge or play it?
if its just to play, all you need to do is to get to the topic with the cartridge and click play on it, simple as that!

You can find and play all cartridges here