No, there is no word missing.
Explanation: The sentence you cited,
(A) Damit wächst in Libyen die Gefahr einer direkten Konfrontation türkischer und ägyptischer Streitkräfte.
boils down to the same semantics as your altered version,
(B) Damit wächst in Libyen die Gefahr einer direkten Konfrontation zwischen türkischer und ägyptischer Streitkräfte.
However, the latter is a slightly different sentence in that it makes something explicit that is left implicit in the former.
In (B), the constellation of parties involved in the conflict is explicitly stated. (B) says explicitly that Turkish and Egyptian armed forces may fight against each other.
Even if we assume that this meaning can only be expressed with "zwischen" (of which I'm not completely convinced, due to the low number of examples e.g. on Duden), the conclusion that "zwischen" is missing in (A) does not follow:
(A) does not explicitly say who may fight whom (although readers will trivially figure this out from context). (A) merely says that there may be confrontations in which both Turkish and Egyptian armed forces are involved. For this statement, using just a genitive is totally appropriate. Note that this is not an instance of meaning 1 from Duden. It is simply a usage of the unspecific noun "Konfrontation" that is then further specified with genitive attributes.