To brew something means to put all the elements together and arrive at a result. You can brew tea, brew trouble, brew a cold, or as in your example, brew an idea.
No, Putin is not referring to drink, but to the way in which these individuals are planning to achieve their own ends.
It is a good example of a practical word becoming one that is used to express concept. It is important not to become too involved with details of the practical aspects when reading something of this kind which is concerned with concepts. Metaphorical uses are not uncommon.
Student or Learner