This isn't just a philosophical game with words. The relativist's view of morality isn't true in the real world either. But we find that the underlying principles themselves are remarkably similar. For example, asked to justify a statement like 'killing people is wrong', they might respond that 'it just feels wrong'. For these people, moral statements are no more than an expression of how people feel.
Morality becomes a matter of subjective taste rather than any absolute standards.
The problem with this view is that most people do seek to justify what they believe to be right and wrong by appealing to their ability to reason rather than their feelings. Let's look at this question the other way round for a moment. A person had killed somebody else. I did it just because I felt like it' to be an adequate excuse. There may indeed be extenuating circumstances, but we would expect them to be based on reason not feeling.