a- in that modifies world
b- proclaiming - why V + ING - useless although some times confusing ,,,V+ING only uses 3 places ,1-gerund , 2-verb , 3-modifiers , here entire sentence part is clause
c- they - pronoun ambiguity
d-
e- proclaimation ? why use NOUN ??? no reason

The Olympic games helped to keep peace among the pugnacious stated of the Greek [u]world in that a sacred truce was proclaimed during the festival's month.[/u]

(A)world in that a sacred truce was proclaimed during the festival's month
(B)world, proclaiming a sacred truce during the festival's month
(C)world when they proclaimed a sacred truce for the festival month
(D)world, for a sacred truce was proclaimed during the month of the festival
(E)world by proclamation of a sacred truce that was for the month of festival

Festival do not posses any month hence festival's month is incorrect - a, b, c ( wrong)
by Proclamation .... that was ... indicates too passive.

Hence the correct ans is D.