The Spanish word "levadura" is a generic term for a leavening agent, which includes yeast, baking powder, baking soda, and cream of tartar. To avoid ambiguity, it is recommended to specify the type of "levadura" needed. For example, "levadura de panadería" refers to yeast, while "levadura en polvo" or "levadura química" refers to baking powder. It is also worth noting that in Spain, "levadura fresca" refers to fresh yeast in cubes, while "levadura de panadero" refers to dry yeast in powder.
When water is added to flour, it starts a chemical process that leads to gluten development. Gluten is formed when the proteins glutenin and gliadin combine with water and form long, curly chains that bond with one another. As the dough is kneaded, the gluten becomes more stretchy and elastic. The gluten strands trap air bubbles produced by the yeast during fermentation, which causes the dough to rise. The yeast feeds on the sugars in the flour and releases carbon dioxide, which gets trapped in the gluten web. The more gluten is developed, the more gas it can hold, leading to a higher rise. Oil cannot replace water in this process, as yeast requires water to activate and become viable for baking. Oil does not hydrate the flour and does not contribute to gluten development. Therefore, it is not recommended to use oil instead of water when making dough with yeast.
The ingredients were probably copied from a Spanish website and included "levadura" which was wrongly translated to yeast when it should have been baking powder. The recipe from the book makes the same mistake using water and yeast when the original Anise Seed Oil Cookies from Carmen Lupiañez don't include water.
Baking powder is activated by moisture and heat, so it helps the cookies rise and puff up properly in the oven. Baking soda needs an acidic ingredient like lemon juice to activate, which this recipe doesn't have. And yet the recipe from "Pastelería Ramos", which is another very popular brand, uses sourdough starter and baking soda according to this video in which they showcase the ingredients.
If yeast is used, it should be in combination with water or milk. When using only oil, you should use baking powder. Otherwise, you could use water/milk and oil and try a combination of yeast and baking powder.
Here is a recipe for Anise Seed Oil Cookies using baking powder instead of yeast, no water, and no liquor:
Ingredients:
- 4 cups (500g) of wheat flour
- 1 1/4 cups (250g) of sugar
- 1 1/4 cups (300ml) of extra virgin olive oil
- 1/2 cup chopped raw almonds
- 1 tablespoon (15g) of aniseeds
- 1 tablespoon (15g) of ground cinnamon
- 1 tablespoon (15g) of baking powder
- Whole roasted almonds for topping
Instructions:
- Preheat the oven to 350°F (180°C).
- In a pan, heat the oil. When it smokes remove it from the fire and add the aniseed, stirring a bit so that it is evenly roasted. Let it cool down.
- In a large bowl, mix together the wheat flour, sugar, cinnamon, baking powder and crushed almonds.
- Pour the oil on the rest of the ingredients and mix well.
- Divide dough into small balls of around 70g, and flatten into disks onto a parchment lined baking sheet.
- Press a whole roasted almond into the center of each disk.
- Bake for 20 minutes or until golden brown.
- Transfer to a wire rack to cool completely.
- Store in an airtight container for up to 1 week.
Tips to obtain even more tender cakes:
The dough should be a bit sticky, requiring some oil on your hands when forming the cookies into balls.
Adding a bit more baking powder would help make the cakes more tender and fluffy.
Use pastry or cake flour instead of normal flour, as it has less gluten content and is special for more tender baked goods.
Be careful not to over-mix the batter. Excess mixing will continue developing the gluten strands into an elastic web, making the crumb tougher rather than tender. Gently mix just until the ingredients are hydrated and combined, but don't beat air into them vigorously. Only mix enough to have a homogeneous batter that is ready for baking. Over-mixing would make the cakes chewier in texture rather than soft and tender.
Replace 50 grams of flour with corn starch. The starch increases the crumb moisture making it more tender. Note that using corn starch will require a bit more liquid in the dough.
Use milk instead of part of the oil to soften the texture.
Bake the cakes at a medium-low temperature, around 160-170ºC so they cook more slowly and turn out more spongy.
When the cakes are ready, cover them while still hot with a damp kitchen towel. The steam will soften the crumb.
The following are some pictures of the industrial version of "Tortas de aceite Carmen Lupiañez" usually known as "Tortas de Algarrobo". There is also a premium version that has an almond on top and as far as I know are only sold on Algarrobo, Spain.

The ingredients for this cookies can be read in English.
GB: Olive oil cake.
Ingredients:
Wheat flour, sugar, extra virgin olive oil (22%), aniseed, cinnamon, almonds and yeast. May contain traces of soy and mustard.
And the nutritional facts are slightly different than for the premium version:
Nutrition facts per 100g
Energy value 1985 KJ/475 Kcal
Fat 23 g
Of which saturated 3,0 g
Carbohydrates 60 g
Of which sugars 20 g
Dietary fibres 2,1 g
Protein 5,8 g
Salt 0,59 g
So, I was mistaken; the cookies are made with yeast instead of baking powder. However, they still do not contain water or liquor, as the recipe from the book La cocina de La Axarquía y sus fiestas by Pablo Castro suggests.