Two viewers have correctly pointed out the same thing:
This isn't actually due to Coriolis, and he did not properly explain the Coriolis Effect anyway. The Coriolis Effect is due to a difference in the speed of rotation of the Earth at two differing points of latitude. The rotation speed of the Earth is greater at the Equator than it is at the poles. The Earth isn't rotating beneath the bullet. The rotation of the Earth is imparted to the bullet. Conservation of momentum. The bullet shifts because the Earth is rotating more slowly, or more quickly, at the destination latitude than the firing latitude.
What he is explaining here is the Eötvös Effect. It is also due to the rotation of the Earth, and also varies with latitude, but it is caused by the centrifugal force that is imparted to the bullet by the Earth's rotation, which is why it is apparent in East-West shooting.
This explanation is wrong. Coriolis effect does not effect a bullet east west, only north south. The Coriolis effect comes from the Change in relative speed of the earth, relative to an object in motion above it. As a bullet fired north from the equator flies, it is travelling both north at 3000 feet per second, and east at 1500 feet per second, a target north of the equator is also traveling east, but at a slightly slower speed, since the bullet is moving both north and east, but east faster than the target, it will, in the same time, travel further east than the target does while in air, striking to the right. In reverse, if you fire from the slower moving target south towards the equator, the target at the equator is moving faster east than the bullet, so it the bullet fired this direction will also strike right. When firing from the equator south, the bullet is traveling east faster and will hit left (in both cases, when firing from a faster moving point on earth, to a slower one, the bullet strikes further east, when slower to faster, further west.)
When firing East / West, a different thing happens, the shooter and the target are moving at the same speed. So when in flight, the target does not actually move up and towards the bullet, when firing west, or down and away when shooting east as depicted in the video. This is just plain 100% false, not arguments about it. Something else is happening to cause the results shown above. When firing east, the bullet is moving in the same direction as the earth, so, relative to the center of the earth, it is moving at a higher degree of rotation around the fixed point in terms of degrees per hour. This causes a greater amount of centrifugal force, which "slightly" counteracts the effect of gravity, essentially making the bullet "lighter" and it will follow a flatter arc, causing a higher "hit". When firing west, the angular velocity or speed of rotation around a fixed point is lower, causing less centrifugal force, and allowing gravity to take more effect, essentially making the bullet heavier, causing a lower hit. This is the Eotvos effect, something tangentially related, but different than the Coriolis effect.
Now, someone should call the author of the video and ask if the bullets were fired EXACTLY due east or due west. If that is the case, the slight horizontal deflections were caused by the wind.
However, if the author of the video says that the bullets were not fired exactly due east or west, then the RE have a huge problem: as has been pointed out, on the western trial the bullets just drop downwards, no Coriolis effect has been measured.