That is funny because tvarůžky is the first thing I thought of when I saw this sentence. I think it is quite good.
It may be offensive and it can just be a joke. It is not used all the time. It is used especially when someone eats too much, too quickly, does strange noises and so on...
Similar to German fressen https://en.wiktionary.org/wiki/fressen.
You can also say tohle žeru as a slang for I like this a lot.
Žere is a rather harsh term for eating; its more closer to "devouring" or "stuffing your face". "Jí" would be appropriate here as a translation for eat.