Is involved in the reduction of 2,3-digeranylgeranylglycerophospholipids (unsaturated archaeols) into 2,3-diphytanylglycerophospholipids (saturated archaeols) in the biosynthesis of archaeal membrane lipids. Catalyzes the formation of archaetidic acid (2,3-di-O-phytanyl-sn-glyceryl phosphate) from 2,3-di-O-geranylgeranylglyceryl phosphate (DGGGP) via the hydrogenation of each double bond of the isoprenoid chains. 2,3-bis-O-(phytanyl)-sn-glycerol 1-phosphate + 8 NADP(+) = 2,3-bis-O-(geranylgeranyl)-sn-glycerol 1-phosphate + 8 H(+) + 8 NADPH 2,3-bis-O-(phytanyl)-sn-glycerol 1-phosphate + 8 NAD(+) = 2,3-bis-O-(geranylgeranyl)-sn-glycerol 1-phosphate + 8 H(+) + 8 NADH Binds 1 FAD per subunit. Membrane lipid metabolism; glycerophospholipid metabolism. Reduction reaction proceeds via syn addition of hydrogen for double bonds. Belongs to the geranylgeranyl reductase family. DGGGPL reductase subfamily.