1) The reason that American Indian land is referred to as stolen is due to the US Government breaking treaty after treaty. For example, several tribes were relocated to the Indian Territory (more on that later), which was fine with the US Government...until it was decided to open it up for settlement, and sell off Indian land to the railroads. The Oglala Lakota received the entire Black Hills by way of the Fort Laramie Treaty of 1868. That was fine with the US Government...until a guy named Custer found gold there in 1873-74......
2) Indian tribes were forcibly relocated during much of the 1800s (Trail of Tears, Apaches to Florida, etc.). The Sand Creek and Wounded Knee Massacres were acts of genocide. Some would argue that what happened to the American Indian was, in general, an act of genocide. Nazis in the 1940s, and (mostly) Serbians in the late 1990s/early 2000s, were tried as war criminals for doing such things (killing of non-combatants based on ethnicity, forced relocation of populations, etc.).
3) American Indians were often forced to attend Indian Schools beginning in the 1880s. Some of these schools lasted until the early 1960s. The primary purpose of these schools was to eradicate the Indian (language, religion, way of life, etc.) out of the person. We didn't demand Germans and Japanese people to stop being German and Japanese after World War II....so to just chalk up the American Indian experience to the "spoils of war" is very disingenuous and intellectually lazy.