I disagree with your judgement. :P
判断 = judgement
裁判 = judgment (and also for 判決, 裁決, 刑罰)
If the intention of this site is for everything to be written in American English, then I guess you would have a point. But I've not yet seen it stated anywhere that the English spelling variety used by this site is American, nor indeed that it is British, Australian, Canadian,...
That said, 裁判 is actually spelt as judgement too on JCJP. I would usually translate this one as judgment instead.
And then there's 素早い, another word in the lessons on this site, which is translated "sharp (judgement)". For this one, I would never EVER spell that word as judgment. :D