I concur with rampy. Nothing at all needs to be done to your monitor to display vertical games, other than placing your monitor into a vertical orientation. There is a bit of overlap in terminology between horizontal games and horizontal monitors. A horizontal game expects the long dimension of the monitor to be horizontal, where a vertical game expects the long dimension of the monitor to be installed vertically.
When most people make mention to a "horizontal monitor", that only refers to the frame style of the monitor. Horizontal monitors typically have a wedge-shaped frame with handles, and then there are "universal" mount monitors that have a flat bar cage around the back of the tube.
Actually, horizontal mount monitors seem to be more common and easier to install because all they need is a shelf to bolt them to, regardless if they are mounted in a horizontal or vertical orientation.
Horizontal mount:
Universal mount:
original Tempest vertical monitor (horizontal mounted sideways):