I think, maybe, you're taking "game" too literally. First and foremost, it's a teaching tool, and throwing you back to the start would actually be counterproductive. It's more of a "fun, imaginary use-case" but "game" sounds better :-)

The levels are small enough that it makes no difference. And as far as teaching goes, repetition is the name of the game. Resetting on failures just means typing the same thing multiple times, reinforcing the things you are having difficulty with. A timer also allows for such things as scoring.

Hmmm... now you've got me wondering. Thing is, on the later levels, I found myself working one property at a time, understanding the effect of that one property, and building up the complete 'answer'. I'm not sure that handling the 'wrong answer' as a special case works for this type of approach. The repetition should (and is, to an extent) be provided by subsequent questions reusing just-learned knowledge.

There's nothing to stop you starting from the beginning at any point, or starting from scratch at any point in future. It makes it less of a 'game' but, like I said, I think you're overplaying the game element.