It automatically advances when you get the answer right. If it's not advancing, you're probably entering the wrong language (even if you think you're right; there are a lot of similar looking, but obscure languages in there). I agree that it would be nicer if the author made it more obvious as to how it worked though.
I thought that too, but it turns out I was confusing two Lisp dialects. At least on Chrome, as soon as you type the correct name, it continues to the next language.