Bingo.
It actually has nothing whatsoever to do with the resolution, only the video signal levels.
Most CGA/EGA (standard res/medium res) arcade games output ~3Vpp video signals, whereas most VGA games output 0.7Vpp (also used by PCs and commercial broadcast equipment) signals. Moving the connector changes some resistive dividers around to account for this difference.
Not really detailed in the documentation is that, should you want to run CGA but from a PC source, for example, you actually want this connector on the "VGA" setting, since you're supply 0.7Vpp signals just with CGA resolution. This comes up when people use emulators on PCs.
If you are, in fact, using different hardware, you probably do need to actually account for this. You can do it separately from the monitor, though. A resistor between your source and the monitor on the RGB video lines of about 220Ω for your CGA and EGA sources (but not your VGA sources) should do the trick. I presume you are using a video switcher or something?