Literally, a calque is a reproduction, a tracing. In particular, (papier) calque is tracing paper. In linguistics, a calque is, well, a calque: a word-for-word translation of a phrase or a translation of words based on superficial resemblance rather than meaning. “Cette formulation est un calque de l'anglais” means “this formulation is a literal translation (a calque) of the English phrasing”. Here, it is meant negatively; this is usually, but not always, the case.
In this case, the English word apply can sometimes be translated to appliquer, and the two share a common root, but the word appliquer cannot be used in the sense of applying for a job. Postuler or candidater (or other formulations such as faire acte de candidature — which sounds really posh for a dishwasher's job) are the usual terms.
This isn't the only mistake in your proposed sentence. “My name is Zolani” should be “Je m'appelle Zolani”. A lave-vaisselle is a machine to wash dishes; the job is plongeur (meaning B). To wash dishes in a restaurant is colloquially called “faire la plonge”.
(Note: I'm French from France; what's wrong and incomprehensible for me may be correct in Québec, but I don't think this sentence would be said differently in Québec.)