Throughout the new Doctor Who (2005) series, you can encounter The Doctor saying that he destroyed Gallifrey and Daleks to stop the universe from burning.
In The End of Time (2), return of Gallifrey disturbed The Doctor a lot. Reason: He didn't want the universe to burn.
In the mini episode The Night of The Doctor, the lady pilot chose to die instead of accepting The Doctor's help. It seemed like she was having bad time due to the Great Time War. Also, in the same episode, Sisterhood of Kahn persuaded The Doctor to finish the Great Time War as if they were severely affected.
In the beginning of The Day of The Doctor, it seemed like The War Doctor wanted to save the universe from burning. But, in the end, it seemed like Gallifrey was losing (Gallifrey was surrounded by Daleks and Gallifrey was only defending with little hope. They also said, "Doctor do something.") and it looked like The Doctor was acting from the side of Gallifrey, not as an authority of the burning universe.
Also, we didn't see ships of any other species in The Day of The Doctor. How was the Great Time War not a normal interplanetary war? How was it affecting the entire universe?