I set off to look at the examples of criticity found by Google (there are 3,120 of them).
I began to feel ill after the first page so I stopped.
I've never seen it before and perhaps will never see it again. But there's no doubt that some people use it in a serious context. For example, Dr Arturo Rodriguez is presenting a paper entitled, Toward a Transformative Teaching Practice: Criticity, Pedagogy and Praxis at a major conference in Chicago in 2008.
I've come across it at work a couple of times in technical journals (I work as an accountant in the health sector) but this is not a word I'd use myself, and I would guess that its use outside highly technical publications would be very rare.