Quickbreads vs Cakes: Understanding Mixing Ingredients - Type 1:  In a typical quickbread (and certain cake recipes), the instructions will say to mix just until combined, no actual stirring or beating. I think this is because (assuming this is made with wheat flour, either white or whole), overstirring or beating would cause the gluten to develop which would result in a chewy texture, not usually desirable in this case.

Type 2:  Then there's the type of cake where the sugar and butter are creamed and then if I recall eggs are added and then the flour. It's not a problem to continue mixing it, in fact mixing is not only okay but required. This tends to result in a light, fluffy cake.

My question: If my premise for Type 1 is correct (overbeating develops the gluten), why does it not hold true for Type 2?
Your premise for Type 1 is correct, however you seem to have misunderstood Type 2: It is no problem to continue mixing the butter-sugar-egg mixture, but as soon as the flour is added, the gluten starts to develop and you should just mix until combined.

For Type 2, creaming the butter and sugar helps to incorporate a lot of air into the mixture, resulting in a light and fluffy texture. This continues when the eggs are added. Proper creaming takes some time, but at some point further mixing does not improve the result any more.