Why adding soda without vinegar to the cake batter?

Both cocoa powder and milk are acidic, and will be reacting with the soda here. Bicarbonate of soda will react with any acid, not only vinegar.

There is also a process called thermal decomposition, where the soda releases CO2 under high temperature without needing an acid, although less than it would in a reaction with an acid and leaving a compound with an unpleasant flavour. See Wikipedia for more detail:

Heat can also by itself cause sodium bicarbonate to act as a raising agent in baking because of thermal decomposition, releasing carbon dioxide at temperatures above 80 °C (180 °F), as follows:[16]

2 NaHCO3 → Na2CO3 + H2O + CO2

When used this way on its own, without the presence of an acidic component (whether in the batter or by the use of a baking powder containing acid), only half the available CO2 is released (one CO2 molecule is formed for every two equivalents of NaHCO3). Additionally, in the absence of acid, thermal decomposition of sodium bicarbonate also produces sodium carbonate, which is strongly alkaline and gives the baked product a bitter, "soapy" taste and a yellow color.

In your recipe, I imagine the soda reacts with the acidic ingredients to avoid this important taste.