Actually, elements have nothing to with nuclear reactions in Chemistry

That’s what it’s already saying, it’s saying elements CANNOT be broken down by non-nuclear chemical reactions. It’s saying what you said in your title.

but it's nothing to do with nuclear energy, someone told me that this definition is wrong. Dictionary.com has the correct definition: Chemistry. one of a class of substances that cannot be separated into simpler substances by chemical means.

Ahhhh, I see.

Nuclear reaction happens only inside the nucleus. When chemical reactions occur elements hold their identity and the nuclei of atoms also remains unchanged. During nuclear reactions, the nuclei of atoms changes completely and new elements are formed. Chemical reaction can be influenced by pressure or temperature.

Source: byjus.com