He dry-labbed the correction factor instead of calculating it, but if the earth was flat, the gun would have been on target without the correction.
He also says the 16" guns did have the curvature calculation built in to the computer (actually a system of gears and cams, a mechanical analog computer.
The accuracy of artillery is well known, Aberdeen Proving Grounds had been doing this since forever, and testing weapons is a world-wide popular thing to do. Every major country tests artillery.
Coriolis was discussed in my web search someone said it was in the software, someone else said it was a tiny error, but I believe it causes a bearing error, and earth curve causes range error.