No, the element is chlorine. Chloride denotes a compound or molecule containing a chlorine ion, or a compound with a non-charged chlorine atom bonded.
This whole thread is very pedantic but in chemistry when someone refers to chlorine, they are usually referring to Cl2. I think in IUPAC naming chloride is reserved for for ions. Like dichloromethane (IUPAC) and methylene chloride (also common name).
I have a phd in chemistry. You are correct. The whole thread is pedantic garbage.