The signal that comes out of a computer into a high-impedance load is 1.5Vpp (actually 1.4Vpp, but close enough). There is a 75 ohm back termination on it which forms a divider with the 75 ohm termination in the monitor resulting in the monitor seeing 0.7Vpp when everything is properly terminated. This is done because the coax cable used has characteristic impedance (Zo) 75 ohms, and terminating everything in this manner prevents reflections and other transmission line end-line artifacts, which can become quite prevalent on even moderate length lines at the high resolutions PCs sometimes run (like 1600x1200). This termination scheme is not often employed in arcades.
If you hook your PC video card straight up to a scope and display a black/white checkerboard, you'll see 1.5Vpp signal levels, but if you hook it up to a monitor and probe the signal lines then, you'll only see 0.7Vpp signal levels. If you drive a PC monitor (or other monitor with input termination) from a low-impedance source such as directly off the output of an op-amp, there's no back termination to divide with, and the monitor will see exactly what you are driving it with.
The choice of 0.7V for active white level has to do with some things you have to do when you AC couple the video and want to restore the DC level, but is otherwise not of much concern in this application. Note that if you have embedded sync on a PC video signal (sync on green), the total signal will be 1Vpp, with +0.7V as the full intensity level, 0V as black level, and -0.3V as sync. NTSC-M (US) plays some tricks and defines the black level to be slightly above blanking which is again above sync. NTSC-J (Japan) does away with this. You can adjust the difference out by tweaking brightness. IIRC, no PAL standard incorporates this "feature".
On monitors where you have control of brightness and contrast, you can adjust some variance back out. Contrast is actually the "white level" adjustment (i.e. you are adjusting what voltage is considered to be "fully white"), and brightness is actually the "black level" adjustment (i.e. you are adjusting what voltage is considered to be fully black). PC monitors often seem adjustable to handle between about 0.5Vpp and 1.25Vpp signals. Arcade monitors are often adjustable much, much further, and TVs sometimes feature automatic gain, especially on their composite input where there are some reference voltages to lock the auto-gain to.
The signal levels of composite NTSC and PAL video are somewhat undefined, also, but people seem to have pretty well standardized on 1Vpp (since it includes sync). It makes the math nice, since full scale is then 1, and everything is otherwise defined as a fraction of full scale. This has to be done since, when the analog signal is recovered off the air, the TV just scales it (using an auto gain mechanism) to something usable internally, as the actual signal level received on the antenna can vary a lot.
Also, as a warning if you plan to build that RGB to NTSC converter, while it should work great [I've built them on custom boards, and while the composite output is only so-so, the s-video looks nearly as good as what you'll be feeding it], be aware that those "crystal in a can" oscillators are often not tight enough for some TVs' chroma PLLs to lock on. I had to build my own oscillator using a parallel resonant crystal and some inverters and tune it up with a variable cap. Also, if you're in Europe, you can set the chip to PAL mode and get something that has PAL style color modulation, but it will still have whatever timings the arcade board uses, which is normally closer to NTSC. Many European TVs will apparently sync up just fine, though.