You are right, it’s complicated. Ballistic doesn’t mean it is a parabolic trajectory. At this distance (I stands for Intercontinental) you need to account for the atmospheric drag, winds, differences in gravity etc. Besides that ICBMs of 1960-1970s were using inertial navigation and had maneuvering warheads (e.g. SS-10), which increased complexity of the calculations. You still can do it on your modern watch.