Strange it might seems, but the intention from Iranian side is to attack the Shipping during the Iran-Iraq war. Both Bogey (by the way, you spell bogey wrong in your OP..Bougey is a disco move...) are planning to ambush the shipping entering/leaving Saudi Arabian Coast.
A news source (I can't remember which) claim the F-4 were jumped by the F-15C and their mission was to ground attack, otherwise F-14 would have ben use. Now, we don't really know if the Iranian Underestimate the combine Saudi/US ability to monitor the area or the Iranian don't even know US were involved in this, but the latter reason seems strange when you consider the information Iranian leak afterward, which is they suspect the Saudi F-15C were piloted by US instructor, it could even be the Iranian simply do not know the US E-3 are in the area operating.
The aerial combat is successful with the Saudi side only because the US is feeding them coordinate and refuelling their CAP. Iranian have more or less Crap Radar coverage and it is not surprising to know if they do not know E-3 are in the Area.
However, what I can say for certain is the JUMPING of their come as a surprise to the Iranian, as after the jumping allegedly occur, Iranian send up 11 more F-4 fighter and loitering the Saudi Border prompting the Saudi to send 11 F-15C in the air to get into stand off.