To 'play favorites' means to treat some individuals better or to prefer them, as when a teacher gives more attention to certain students or gives them better grades/marks than other students who have done the same quality work.
'Playing of favorites' is just a gerund variant of this idea.
Right. Note that the phrase is "play favorites", as in "George played favorites when he chose his team," and "George was known for playing favorites when choosing his team." "Playing of favorites" is grammatical, but almost never the best usage.