It is murder alright. However, she could be sitting facing any direction hence the splatter of blood is not enough evidence. And because the gun is in her right hand does not mean she is right handed. She actually looks left handed. Check the position of the pen beside the letter. If you are left handed you drop the pen on the left hand of the letter. To add to that, her ash tray, pack of cigarette and coke can are all on the left. She is left handed and the gun is in her right hand; that's murder right there.
This is murder because if she was sitting and shot herself and considering she is right handed the blood splatter should be in the opposite direction and not there. So it means I was murder and somebody wanted it to look like suicide.