This recipe is a cheat. A true snickerdoodle is a refrigerator cookie. The battery dough gives a very specific texture. This one comes close without the wait.

The creaming step is one of the catching points. Over doing it will make more of a shortbread.

I shall quote the big book:

Creaming Method
This is nearly identical to the creaming method for cakes. Because cookies require less liquid, it is not necessary to add the liquid alternately with the flour. It can be added all at once.
Note the importance of step 2, the creaming stage. The amount of creaming affects the texture of the cookie, the leavening , and the spread. Only a small amount of creaming is desired when when the cookie must retain its shape and not spread too much. Also, if the cookie is very short (hight in fat and low in gluten development), or if it is thin and elicate, too much creaming will make the cookie too crumbly.
— Wayne Gisslen, Professional Baking, 4th Edition

Another thing I like about this one is you can replace the cinnamon with lavender, rosemary, cardamom, even a chai blend.