You're vastly overstating the function of the EIU. It's an interface unit. it doesn't tell the ECU to DO anything. It merely "tells" the ECU what the positions and demands are from the various items with which it interfaces. The ECU then applies the necessary actions which are required according to its internal logic.
The main reason for the EUI is to reduce the amount or wiring and therefore weight. If it were'nt there, every discrete switch position and data bus which feeds it would instead have to go direct to the ECU on the engine so there would be alot more wiring and cable looms.
So for example, the engine anti-ice switch position determines whether to open or close the anti-ice valve. Not the EIU or the ECU. However, because the switch is selected on, the EIU indicates this position to the ECU and the ECU then demands continuous ignition (and an increased fuel flow if the engine is at idle).
If the mode selector switch is in ignition/start in flight, then the switch position is indicated to the ECU by the EIU along with the air/ground status, that is all. The ECU then commands continuous ignition.
The arrows on the diagram indicate the direction of flow of information/discrete position which helps a little with figuring out what's happening.