I'm a little surprised there aren't more DIY RGB to VGA converter boards.
It's actually a somewhat complicated process.
There are a few ways to do it, and the "optimal" method depends on your input characteristics (progressive ~240 line or interlaced ~480 line) as well as your desired output characteristics (crisp pixels or something more smooth). Pretty much all techniques require that you digitally sample the video, store it in RAM, possibly do some stuff to it, then clock it back out at a different rate than it came in.
Note that VGA *is* analog RGB. It's electrically very, very close to what an arcade board outputs. The signal levels are a bit lower (0.7Vpp instead of 3.3-5Vpp), and VGA generally uses separate sync rather than composite, but composite sync is not unheard of an is supported by many monitors. The issue is that standard res arcade games run at a lower horizontal scanrate (~15kHz) than most PC monitors can sync to (minimum ~30kHz). Effectively, to get standard res video on a modern PC monitor, you have to "scale" it in one way or another.
I've built stuff to do this before. You need a video CODEC or separate ADC/DAC pair, some RAM, and something to handle the processing (FPGA or DSP). These tend to be "large" parts in non-DIY-friendly packages (fine pitch surface mount or even BGA) and have some funky power requirements.