A definition need not meet the legal bar for us to consider what kind of things a formally specified law might include; there are doubtless many possible definitions of 'hate speech', and debating those and reaching an agreement among various interested parties is part of the legal process that involves the whole of society. Someone is going to disagree with any definition given, but that doesn't mean that the sovreign lawmakers can't come to some agreement when put to debate.
In other words, unless the person you're replying to is a lawmaker with supreme authority, there is no need for them to speak for what you might have 'hate speech' defined as in law. Most people aren't lawmakers, but they are involved in the process of creating laws.
https://www.adl.org/resources/hate-symbols/search
Looks like they involve discrimination (on race or religion or such). But Japan's new law is more general.