No don't slip any sts. The greyed out blocks don't represent sts. They're just place holders. On later rows you'll be increasing sts and the grey blocks will disappear as the increase sts take their place.
So for example, on row 1, purl 13sts, M1, CD1, M1, purl 13sts. That'll use up what I assume are the 27 starting sts according to the note below the chart.
Your photo uploaded well. Maybe this afghan in squares?