Togo out of your way literally means to deviate from your normal or intended route. Figuratively it means to put more effort into doing something than is expected or is usual. Here it suggests that he would be very alert for ways his opponent might attack him, or watchful for moves by his opponent that might indicate an attack was developing, and would respond immediately
I think it means he would mentally influence him before the game starts. And for this mental influence to take affect he would do his very best. OR That in terms of the game he would play very defensive just to stop the attack, before the game gets any momentum.
I think it also depends on the full context. Are they already playing?