monitors were mounted differently in different cabinets and different mfg assumed different orientations.
Therefore some older games require the monitor to be rotated correctly.
GENERALLY, a horizontal game will work with any horizontal monitor that is mounted with the anode cap facing up.
However, a vertical game will typically vary depending if you rotate the monitor left (counter clockwise) so the anode cap faces left, or right (clockwise) where the anode cap faces right.
Newer vertical boards typically include a dip switch to draw the graphics rotated 180 degrees so you don't have to rotate the monitor.
The "quick fix" for a badly oriented monitor in vertical orientation is to flip both pairs of yoke wires.. red for blue and yellow for green. However this *can* lead to a slight change in color and convergence, so you should inspect the image with a pattern generator to ensure it is correct in the rotated mode.
No game can convert the output of a horizontal to vertical and vise-versa.... EXCEPT for the mame emulator itself (the real boards can't).
As to why you might have a mirrored image (only one set of yoke wires flipped, not both) is that some games actually have the monitor mounted face up, right behind the coin door, and use a mirror slanted in the back facing out. This allowed additional graphics or other effects taped on/around the monitor or projected onto the surface.
A common one like Kick(Man) comes to mind as that was used in their upright. Some newer (late 90's) games include some rifle/shooting ones. I think there was some black and white ones from the mid 70's that used them too.