I don't understand why you understand it here. You wrote and I may quote you here again;

If IPS = IPC*time and AMD has the highest IPC how come Intel has the highest IPS ? According to the formula if you have a greater IPC you should also have a greater IPS.

Intel has higher IPC since it clocks higher – and with that clock-speed advantage, Intel has a higher resulting IPS, despite they have a lower actual IPC.

You didn't tell me what I did get wrong.

I did in fact, as I already started my very post with the thing you were overlooking – the thing about the clock-speed.
Intel literally compensates a lower IPC through higher clock-speed – It's really that simple.