Many people pray through Jesus because of John 14: 13&14...
Jesus instructs the disciples to pray in His name... and He tells them that whatever they ask He will do...
Yet the chapter also makes mention that the disciples will do great works, greater that Jesus performed...
I can't say with certainty why people who are not Christians are answered. I do have a theory...
Maybe, we ask in Jesus name when we are praying for others that we may show the glory of God...
But when we are praying for ourselves, maybe we are supposed to follow the example that Jesus set, and pray to the Father (The Lord's Prayer)...
Those who are not Christian may be answered because they are praying for themselves to God, and God answers them because they are seeking Him earnestly the best way they understand how to.