The risk premium is measured as (1+Market Return)/(1+Treasury Yield), or approximated by Market Return - Treasury Yield. The GGM is just another way to estimate a forward looking return on the market. This methodology is known as an ex-ante risk premium. If you were to measure the historical risk premium, this would be an ex-post risk premium. The GGM method is a way of measuring what the investment community is expecting the risk premium to be, the ex-post method is a way of measuring what the risk premium actually was.
Total market return is measured by capital appreciation, and dividends recieved, hence long term earnings growth according to the GGM should be the same as yearly capital return, then you add the dividend yield and subtract the risk free rate.