The analog vga connector (15 pin's 3 row sub d) has some pins that are used to query the monitor and find out what resolutions it supports.
It also tells the computer what the optimum resolution of the monitor is. it's basically a small memory chip that uses the IIC protocol interface.
It's also called the edid information of a monitor. Your arcade monitor probably isn't providing this information to your pc. If the information is missing, your pc might start to use a standard resolution preprogrammed in it's bios. For the more modern pc's, this can be 800x600, as that's also the smallest resolution still capable of showing most os windows. If your monitor still supports it, you can try a 640x480 resolution on your pc, and you will notice that it's hardly workable. The OK and Cancel buttons usually present on the bottom of a window simply are off screen. You can't move it with your mouse as you need to click on the top bar for that, and that get's off screen when the bottom is in...
To my knowledge, there exists small boards with the memory chip you can connect to force your computer to use the 640x480 resolution.
Another thing you can test is booting the computer with an lcd, setting the resolution to 640 x 480 and connecting the arcade afterwards. Once the os is started up, it shouldn't switch resolution anymore. It would prove if the theory is correct.