I think the worldbuiding in that otome game isn't catering for realism but for certain vibe to exude towards players of the game. Just like in some media that has weak worldbuiding with things that exist in the world because they are cool. I would think that abascus desn't exist just because it isn't romantic and it doesn't fit.
The game likely does not have any math in it anywhere, so the world does not include any of the tools that would be required to even have things like buildings as that's not part of the sexy magic vibe.
Yeah, that's a bit strange. By the time a similar time period came like in the anime, the abacus was already pretty ancient, albeit not in the form we're familiar with (though that definitely existed in Europe too by then)