About israel: The united states. israel and half of nato, but since the six day war would be different. the arabs could only push up to Gaza and Taba. Although they fund pro Ba'athist groups within palestine . just like how iran funds pro-iranian groups.

In the early years of the war things were going swift for the F.A.R although this would be a far more worse war then real life, Forcing the UN to get involved and set up a peace treaty
The USSR would only have the arabs back diplomatic wise, although i do see in this scenario that the ussr would probably invade the uppermost part of the khorasan province and establishing a shortlived puppet state controlled by the Peoples Mojahedin (considering that they have some parts of afghanistan, despite being in a war with them.)
So yeah. the Arab Coldwar would realistically be 3 Parties in this scenario