EmulationStation has the X button mapped for choosing a random system or game. If you're in the system list, X will position you to a random system, if you're in a game list (inside a system), it will position you to a random game - you just have to press A to start the game.
Modifying the existing behavior - to start the game automatically - means you're going to have to program it into EmulationStation - something that's non-trivial for someone that's not familiar with programming or EmulationStation's source.