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. Can use both NADH and NADPH as electron donors. Also catalyzes the reduction of the naturally occurring 2,3-di-O-geranylgeranylglyceryl phosphate derivatives such as 2,3-di-O-phytyl-sn-glyceryl phosphate (DPHGP), 3-O-(2,3-di-O-phytyl-sn-glycero-phospho)-sn-glycerol (DPHGPG) and 2,3-di-O-phytyl-sn-glycero-phosphoethanolamine (DPHGPE). Is not active toward 2,3-di-O-geranylgeranylglycerol. 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. Monomer. Reduction reaction proceeds via syn addition of hydrogen for double bonds. Belongs to the geranylgeranyl reductase family. DGGGPL reductase subfamily.