Genocide is defined as the intentional destruction of a national, ethnic, racial, or religious group. This definition is set out in the Genocide Convention, which was created by the United Nations in 1948.
Acts that constitute genocide
Killing members of the group
Causing serious bodily or mental harm to members of the group
Deliberately inflicting conditions of life that will lead to the group's physical destruction
Preventing births within the group
Forcibly transferring children of the group to another group
Prosecution of genocide
In the United States, genocide is prohibited by 18 U.S.C. 1091.
The United States has federal jurisdiction if the offense is committed within the United States.
The United States also has federal extraterritorial jurisdiction if the offender is a US national.
Proving genocide
Proving genocide can be difficult because it requires showing a specific intent to destroy a group.
The intent to destroy must be shown to exist in respect to a substantial part of the targeted group.
I agree with your take on this by tying the stealing of land, homes and forcing any ethnic group to leave their homeland via violent means to the actual word genocide with some language alteration to distinguish it from actual extermination.