No, it's not. It's better than "Κλείστε" as a matter of fact, good thinking! :) One minor thing: you will really hear it as "Κλείσ'το!", the ε is dropped all the time in this case. Same with Κάν'το (Do it), Πάρ'το (Take it), Φά'το (Eat it). If it is two syllables, you drop the ε, if it is more, dropping it is optional: Διάβασέ το or Διάβασ'το (Read it).
This tradution is wrong! The say κλείστε το but the accept just close as correct and it is not!