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. 8 A + a 2,3-bis-O-phytanyl-sn-glycerol 1-phospholipid = a 2,3-bis-O-(geranylgeranyl)-sn-glycerol 1-phospholipid + 8 AH2 2,3-bis-O-(phytanyl)-sn-glycerol 1-phosphate + 8 A = 2,3-bis-O-(geranylgeranyl)-sn-glycerol 1-phosphate + 8 AH2 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. Truncated N-terminus.