An even game of go is a game played without handicaps.
These days 'even game' is nearly the same as 'game played on an empty board'. One wouldn't call a game with a large value of komi even - but this isn't a system used in serious events. The old starting positions used in China and Korea for hundreds of years up to the period 1930-1940 were with the board set up to a standard pattern. In China, anyway, this was varied to give handicaps, and an even game was one using the Chinese classical opening.