"This is not a game."
Translation:Ez nem játék.
More unusual than wrong. It is much more common this way. Like "This is no game". Btw, "játék" means both "game" and "toy". But not wildlife.
Sort of - nincs is literally the irregular conjugation of nem van (which is never used) Nincs is used in the sense of there is not/does not have because van is used in this sense also, but is literally is not: for example, ő nincs itt = (s)he is not here
So Ez nincs játék is wrong because equality of two nouns (or a noun and an adjective) requires omitting van (and by extension, omitting nincs - but of course keeping nem, because otherwise you would have no idea there was a negation)