This is a simple and obvious definition, but apparently too complicated for some feminists who, in the drunken-with-power glory days of feminism, insisted that domestic violence was the process whereby all men oppressed all women through threats and acts of force.
Apparently it was only domestic violence when a man assaulted a woman. When a woman assaulted a man, or when a woman assaulted a child it was not domestic violence. This is an example of definition hijacking. By taking a word and redefining it to mean something else, or limiting its use, you can stop people drawing conclusions that you don't want them to.
The domestic violence which is discussed the most is men assaulting their partners. In fact this is the easiest kind of domestic violence to avoid. The easiest way to avoid this is for women not to marry violent men. The simple fact is that many women (mostly young women, but older ones as well), are attracted to men who are violent. One only has to look at the number of women desperate to date footballers, and men from other violent sports to see the correlation with violence. In some circles, the highest status that a young woman can get is two men fighting over her. The more blood, the higher the status.
Is is any wonder that ten years into such a marriage, that the violence turns against the partner? The man is then not as powerful or strong as the younger up-and-coming generation, his propensity for violence has not helped him in his career (probably quite the opposite), husband and wife see other people achieving far more (that nerdy guy in school with the weird ideas now drives a Ferrari). The only way he can express himself is through violence - against guess who? His wife.
There is much discussion about what should be done about domestic violence, and how to handle it. Ultimately it is not up to others to make judgments about the private behavior of adults. Initiating violence against people is crime, but there are many dangers in judging that this has happened without a complaint from a supposed victim.
Maybe they are playing a weird sado-masochistic game, maybe they enjoy beating each other up, maybe it was some weird misunderstanding, maybe they don't really think it is a big deal. Clearly if there is a complainant, then the issue becomes more straight-forward.