I have never ear about using GMEM instead DMEM to grow mES cells. We have always use DMEM + 15 FCS + P/S + 2mM Gln + NEAA to maintain our cells w/o compromising their ESc properties (Bibel et al., 2006 Nature Protocols)
Both GMEM and DMEM are commonly used for mouse embryonic stem cell culture. GMEM contains half the concentration of amino acids and vitamins as DMEM (and also omits glycine and serine). DMEM/F-12 is also sometimes used for mESC culture, and contains additional supplements such as biotin, B12, thymidine etc. These basal mediums can come with further adaptations, e.g. high or low glucose, with or without pyruvate, with or without HEPES.