Game capture problem

[ALAINGG_]

Hi everyone, i want to make stream from this game and for that i use a gaming computer and a stream computer using a game capture from elgato to do it. The problem is that a second HDMI cable is conected to the gaming computer so its like a second monitor, so the game its just not working correctly, has a lot of lag frame drops. I know that removing the second monitor cable the problem its fix (i already check it) but i want to stream with the other computer and i need yes or yes connect a second monitor cable from the gaming computer to the elgato Game capture. Somebody knows how to fix that without leave just one HDMI cable?