Found the issue! It turns out that in creating the wall with the AddWall() function, the width property was not set correctly.
Casey had the following code.
Entity.Dormant->width = Entity.Dormant->height;
But, I instinctively typed the following code around line 343 in handmade.cpp
Entity.Dormant->width = Entity.Dormant->width;
This wouldn't actually draw anything, because it wasn't set to anything. If I wrote the following, there wouldn't have been a problem.
Entity.Dormant->width = GameState->World->TileMap->tileSideInMeters;
Since the problem has been solved, I'll be taking down my code. The image demonstrating the original problems will still be available.