The quote is about the despair and hopelessness the father feels at the doomed situation he and his son are facing.
The Earth and the blind dogs of the sun in thier running are the planets in thier endless orbits. The universe is godless and unthinking and as such there is no salvation coming, things are as they are and will not change.
It mentions the 'intestate earth' meaning the earth has died and has nothing left of use to pass on to an all but dead human race. The game is up!
The two hunted animals are the father and his son, the references to 'borrowed time, world, and eyes' are references on the fact that the end is likely near. Borrowed time and world, the world will soon be lost to them and borrowed eyes meaning that after thier deaths their bodies will decompose and return to the fabric of the earth.
Pretty gloomy stuff. This is all taking place in the fathers thoughts at that time though, at the end of the book we find out that there is a small glimmer of hope left.