The text is difficult to understand fully, but it appears to be a portmanteau of philosophical and fugal
: of, relating to, or being in the style of a musical fugue
1 a : a musical composition in which one or two themes are repeated or imitated by successively entering voices and contrapuntally developed in a continuous interweaving of the voice parts
b : something that resembles a fugue especially in interweaving repetitive elements
2 : a disturbed state of consciousness in which the one affected seems to perform acts in full awareness but upon recovery cannot recollect the acts performed
That leaves us with two possibilities: either this kind of film analysis is repetitive and contrapuntal and interwoven, or else it resembles a fugue state. Neither meaning obviously fits, but either one seems possible.
In case anyone else wants to take a stab at a broader analysis, the quotation comes from here: "Calm - On Terrence Malick's The Thin Red Line"