Hanley: But you don't even care about the art!
Bronsky: But you do. That's good enough for me.
Hanley: I don't know what you mean.
Bronsky: I think you do.
Bronsky uses the word "philistine" which has different meanings but in this case, he probably meant the derogatory term used to call a person someone who despises or does not understand the value of art, beauty, or intellectual values. So for the context, it fits.
TitleThe Art of War is an allusion to the famous writings of an ancient Chinese general Sun Tzu (also known as Sunzi or Sun Wu), which is considered to this day to be essential basic knowledge on military strategies, pro sports team play and business success.