The Supreme Court held a conviction for simple battery against a domestic victim triggers the prohibition against firearms possession at 8 USC 922(g)(9), a federal crime. Immigration advocates had feared that a holding along these lines would be used to justify expanding the domestic violence ground of deportability to also include simple battery against a domestic victim--making deportable, for example, an immigrant convicted of the misdemeanor offense of pushing his wife.
Fortunately, however, the Court explicitly stated at footnote 4 that nothing in its decision should cast doubt on precedent that holds simple battery against a domestic victim does not implicate the deportability ground. The court recognized that the deportability ground incorporates the generally-applicable "crime of violence" definition at 18 USC 16, which the Court has repeatedly held applies only to the active use of violent force capable of causing injury.
The criminal statute in Castleman did not include that reference to 18 USC 16, so the Court applied a much more expansive definition of domestic violence, over Justice Scalia's objections. It cited arguments and statistics by advocacy groups and the Department of Justice to explain why a simple battery that would not be considered "violent" in the ordinary sense is "violent" when it occurs in the domestic context, since it often occurs as part of a pattern of intimidation and control.