Yarb:
Your TV would likely not work without hacking, unless it has an SCART connector (e.g. if it was a high end set sold to Audio/Video production companies it might have it.. I've seen the 19" JVC version of the 13" Commodore 1702 monitor at thrift stores before, dontated by local TV stations..they had SCART connectors on them).
RGBI is "digital" (aka "Intensity" bit) RGB, where RGBA is "analog" RGB.
Basically all TV/Monitor tubes take Analog signals, and that's what Arcade boards put out--NOT analog. However, some monitors were built with a Digital interface to the outside, and converts it to analog inside, but not offering analog to the outside.
This is what my Commodore 1902A model by magnavox was. It had a daughter board that converted Digital RGB to Analog RGB. Simply take the board out of circuit by cutting traces to it, then feed in the analog where it output the converted.
Arcade game boards all put out (to the best of my knowledge) Analog RGB.
Digital RGB works as follows:
Each wire (R,G,B) specify either a 0 volt or 1 volt signal. 0 being off, 1 being on. Therefore with Digital RGB that's 2^3 = 8 discrete colors. However, a 4th line called "Intensity" (I) was added. When it is 0 the color is at half brightness, when 1, it is at full brightness. This means 2^4 = 16 discrete colors. Thats why computers like the Commodore 64 and original IBM CGA graphics were limited to 16 colors.
Analog RGB works by an "unlimited" (theoretically) variation of voltage. Computers work in the 0-1 volt range (Commodore Amiga, VGA, etc..) Arcade boards worked in the 2-4 volt range.
The higher the voltage, the brighter the color. But totally variable. Therefore it's no longer digital, and theoretically unlimited (or at least 24 million+ colors as the human eye can discern)
Therefore to connect an arcade board (or special VGA adaptors that can sync down to 15.75 KHz horizontal for TV use) you need to get the analog signal out into the analog signal in of the monitor. And if it's not an authentic arcade monitor supporting the higher voltage range, then you'll need to reduce the voltage to meet what the monitor wants, as I previously aluded to.
Again, hacking into TV's/Monitors is a very interesting project, but please don't do so unless you know what you're doing. Don't entirely trust what someone else writes on the internet. Do your research. Understand voltages, resistance, capacitance, isolation, etc... before you start such a task.
Oddly enough though, of course, your arcade board AND computer initially work with video VIA digital RGB, either 4 bit (16 color) 8 bit, 24 bit (24 million colors) or 32 bits. Just before what your game draws leaves the board, it changes the digital signals into analog ones to feed to the monitor.
PS: You CAN send analog RGB output into some digital RGB inputs, but you'll be left with only 8 colors, and likely washed out or too dark too. So unless your game only draws in 8 colors or less (not very many!), you'll need Analog RGB inputs.