How does the order of mixing ingredients affect the resulting cake?
I'll try to break this down into components to make it simpler.

If a recipe starts by combining sugar and a solid fat (creaming), this incorporates small air bubbles into the batter which will be seed bubbles for the carbon dioxide produced by chemical leavening. Occasionally, this creaming is used alone for leavening (as in traditional poundcakes).

If the flour is added straight to this, it can help prevent the batter from curdling later if a colder ingredient is added. This also coats the flour with fat, preventing gluten development and making a very fine, tender crumb since the flour is "waterproofed" before other liquids are added.

If eggs are added to the fat and sugar, you can make an emulsified cake but the presence of water when the flour is added can make it slightly tougher.

Some recipes (usually with oil) require all the liquids to be mixed together, and then added to all the dry ingredients which have already been mixed. Again, this can sometimes lead to a tougher cake since the flour is exposed to water. 

Another method is to mix all the dry ingredients, then incorporate the solid fat into that, then add liquids. This will usually lead to tender cakes as the flour has been coated with fat before liquids are added.

If a cake is leavened with whipped egg whites (or whole eggs), those will be added last to prevent the bubbles from being knocked out by excess stirring.

You pretty much always want the fat to be present when the flour is added though. As you saw in your recipe, adding liquid to the flour without the fat will allow too much gluten development and make your cake tough and dense.