No, please read the Tips & Notes at the top of the lesson page.
Dreng has only one syllable and is a common noun and is regular so it gets 'e' at the end, as those usually do. If there were already an 'e', there would not be an additional 'e' added.
Pige is a multiple syllable noun that already ends in 'e' and gets 'r' added to it. If a multiple syllable noun does not end in 'e', then 'er' is usually added. Neuter nouns with one syllable usually don't get something added to it.
Here is a grammar reference that they are working on also: https://www.duolingo.com/comment/4277767
This is tough. I couldn't even get this far without having completed the Swedish tree. Min svensk farfar warned me about Danish. I'm going to make a bowl of oatmeal now, and when I get to the next pronounciation exercise I'll have a mouthful of hot oatmeal! Kierkegaarde I have the reason for your pessimism.