Periodic desertfication of the broad north African region north of the Sahel is a notion that dates back to at least the early 1980s (and probably decades before) and is based on layering in river systems and other strata evidence.

This specific research tightens up the timing and driving factors for the specific Sahara region (Libya, Egypt, Sudan) and doesn't relate to the Arabian Peninsula which is an almost seperate landmass more than three quarters surrounded by sea water.

On that landmass the Arabia Felix region (modern Yeman (mostly)) is known to have been greener in the past.