My Greek native husband claims you can also use this phrase to mean "That is a plate"
It is one of the alternative translations.
Partly, you are correct. The pronoun is not necessary in Greek (just like in Spanish. I noticed you're taking the Spanish course too), so it is only necessary when it's translated as this/these.
However, in the first few skills, the pronouns are included for the sake of teaching, so that the learners and get a bit used to them. It could be hard for people that have no knowledge of Greek to drop articles from the very start. :/