The minimze button minimizes the app to the systray, the x will close ICQ down, these are generally just default widgets.
Did you look into the preferences and try any of those to see if they will make a change? I know there is AUTO-HIDE, which says it will minimze to the taskbar, but when i enable it is does not send it to the taskbar, just to the systray
I know the message dialog box will move to the taskbar, while the contact list can minimize to the systray (where the clock is and flower icon) This is why there is a minimize button, so you can send the contact list to the systray.
Did you look on the icq website, that would be your best bet in trying to find a solution, since they should have created a complete FAQ section for users.