Also, maybe someone should check how many letters total would it be typing out all 120 levels' names? It would give a better idea what kind of typing speed is required (given the quiz's current time limit) just to type all level names out when you have the entire list in front of you!
I got bored and decided to calculate the above, with the help of Excel and Word. Copy-and-paste a complete list of level names (eg. try Googling "lemmings-walkthrough.txt"), use Excel to extract out just the column of level names, and then use Word's search/replace to remove all non-alphanumeric characters (because the quiz doesn't care about punctuation and spaces, eg. you can just type "justdig" instead of "Just Dig!"). Also remove duplicate instances of "We all Fall Down" (since the quiz will automatically populate all 4 instances of the level when you type it out just once). Finally use Word's "word count" feature.
This comes out to 2005 characters, or 401 "words" (in the technical, typing-speed sense of 5 characters per word). With 7 minutes, this comes out to a required minimum speed of about 57.3 words per minute (wpm).
Wikipedia says "an average professional typist reaches 50 to 70 wpm".
So typing out the whole list of levels within the quiz's time limit is definintely humanly doable, though that alone may be a slight challenge already if you are slow at typing.