You're not missing anything. The motor develops a torque, and the torque has to be countered by two forces offset from each other. The rope can be one of those forces, but another is required to keep the body from moving.
This. Clamp or weld a bar to the drum, secure the bar, and the winch will try to spin only, without pulling the bar in.
Once the bar hits the winch frame/cross bars, if they're are strong enough to stop the motor, the forces become internal again and the winch will sit peacefully even though the internal forces are very high.
Rope makes a really bad wrench handle. It can't transmit torque, just tension. So we draw our little magic black box around the winch and we only have to analyze the attachment points: rope on the drum and bolts at the feet. The rope only transmits tension so the only reason the winch tries to rotate is because the feet are offset from the rope.
Now if you had 2 lines coming off the winch, one forward and one back, and equally loaded, the winch body would only try to spin much like if there was a bar welded to the drum. The feet would only see vertical forces as the 2 lines would cancel out the horizontal forces.