How does the order of mixing ingredients affect the resulting cake?

I wanted to bake a Devil's cake yesterday. I got my recipe from a trusted book and I was surprised to see that the order of mixing was as follows: sift together flour, sugar, baking powder and salt, then mix eggs one by one. Then butter, then other ingredients.

This is contrary to the process I was used to i.e. butter & sugar, then eggs etc.

I was suprised to see that the eggs mixed very good and that, in the end, there was no sugar granules had remained. I was not suprised to see that the resulting cake was dense.

But it still baffles me. I guess there are different ways to mix a cake, depending on how you want your cake to be. Like, flour first -> dense cake, eggs first -> light cake, butter first -> standard cake.

While I can understand that beating the eggs first traps air, what the other methods do is not clear to me.

So, what result do the different mixing strategies give?