I'm reading Oren's Six Days of War and came across the passage:
Thus, the proposed union of Egypt, Syria, and Iraq was presented first and foremost as a coalition against Israel because, for all their ideological affinity, there was no other issue on which all three could agree. Egypt portrayed its intervention in Yemen as a “step in the process of getting rid of Zionism,” while the Jordan-Saudi (Ta’if) pact opposing that intervention signified “a front against Jewish aggression.” - p. 18
I'm not able to find either of his references for his quotes, and I don't get what the war had to do with Zionism at all, let alone how both sides (the Jordan-Saudis, and the Egyptians) could each see their position as opposing Zionism. Maybe I'm reading this wrong?
An understandable conundrum!
The idea is merely that the sides somewhat split on the Egyptian-Yemen War, between the Egypt-Syria-Iraq axis and the Jordan-Saudi axis, and both had different ideas of what should happen in Yemen. As a result of these differing ideas, both sides tried to play to their populaces in the best way they could: blame Israel. This tactic was taken quite often with the Arab states, who wanted to drum up support for their policies while also being perceived as not forgetting about the Israelis. The Arab states are often said to have feared "the street" (ie. the public) as much as Israel itself, so they often worked to create a common external threat (Israel being a convenient scapegoat) to justify their actions.
This tried-and-true method was likely employed here, as you can tell by his quotes (assuming the quotes are correct, I unfortunately don't have those books on hand right now). I think you are misreading in that you say the "Arab world" was united against Zionism by the war: the war did not unite the "Arab world", but united some factions of it. Jordan was actually fairly reluctant to enter the 1967 war, and did not really seem united with Egypt and Syria in the pursuit. The Egypt-Yemen war provided not only a context for blaming Israel for more problems (taking an unpopular intra-Arab war and saying Israel was at fault, to make it more popular) but it also provided a context for Egypt and Syria to become closer and form the coalition they had against Israel which was much more anti-Israel than the Jordan-Saudi axis.
That, I think, is what Oren is referring to.