That author talks about centrifugal force, which is sometimes referred to as an inertial force or a fictitious force. This is because it’s really just a result of measuring motion from a non-inertial reference frame. What that really means is that it’s not necessarily a force at all, but a change in motion of one object with respect to another due to the reference frame accelerating.

Take the car example- the author describes you driving a car around a corner, and you feeling a force throwing you outward. There is no force that does this. What is really happening is that your body had momentum going straight. If the car were to suddenly vaporize or disappear, your body would keep going straight until it hit the ground and started tumbling. So your body wants to keep going in a straight line because it has forward momentum. When the car turns, it’s “forcing” (see what I did there) your body to change direction, which changes its momentum. What you feel is the centripetal force coming from the car pushing your body toward the center of the radius of the turn.

The earth is similar, in that it changes its direction, but because the bullet is not connected to the earth, like your body is connected to the car, the bullet does not move with the earth, so when the earth drops down a bit, and the target with it, the bullet does not follow the same motion, and continues on its original trajectory, causing the target to drop out from under it. You could discuss the effects of this motion in an inertial reference frame, and use forces like gravity to do so, but I find the inertial description much simpler and easier to understand. When the bullet is in flight, the earth/target drop out from under it, or they rise into the bullet, depending on which direction you’re shooting.