I thought I saw all versions of RBI, until I stumbled upon this youtube clip...is this part of the pro yakyu series or something? It looks like 16-Bit graphics...basically RBI with SNES graphics...
http://www.youtube.com/watch?v=TDrzY2cvSV4&feature=related
Looks like one of the Super World Stadium arcade games - I've downloaded and played a few of them on MAME. World Stadium was the arcade version of Family Stadium, as far as I can tell, and it became Super World Stadium when they moved to SNES-quality hardware.
They made annual releases of the series - from looking at the games list on PlanetEmu.net, World Stadium had '89 and '90 releases, with Super World Stadium taking over for the '91 version and releasing annually until 2001. I remember trying the '99 version on my computer a few years ago (it was the newest MAME-supported version at the time) - it had a complete graphical overhaul, with 3D graphics instead of sprites and a different batting perspective (more behind the batter). It was pretty choppy, so I didn't get to try out the gameplay at all, although it might be better now with a more-recent system.
(http://planetemu.net/screenshots/mame/sws99.png)
Same Katakana beginning as Famista (aka family stadium) so part of the same series