You suggested that one of the problems with having another offence here is that the definitions of torture are different. It seems to me that the nature of torture in the two circumstances is different in any case.
For example, for state torture, part of the definition is the purpose for which these acts are committed, such as attaining from a person or from a third person information or a statement, or coercing them to do something, and so on and so forth. However, in the case of private torture, it seems to me there is much more of a likelihood that the motivations are about revenge or about some sadism, or some other kind of unsavoury thing beyond what the state might use it for.
In that context, are separate definitions legitimate?