Sure, those terms are used in the paper. In general, open-loop vs. closed-loop refer to systems without and with feedback, respectively. Previous studies already showed that high-frequency stimulation could improve memory. Those were open-loop because they didn't use EEG feedback; stimulation is always on. The alternative is stimulation only when the subject is predicted to forget the word, based on EEG feedback.

The obvious question is whether EEG-based stimulation makes any difference compared to always-on stimulation. It is very possible that the difference is negligible and that the EEG feedback doesn't matter.