In a vacuum, I would not say that's hate speech. But there are complexities in the advocacy for capital punishment in the current context of the US's criminal justice system.
Our carceral system is widely recognized to be deeply racist in practice and in philosophy. This being the case, it's not an unbelievable stretch to say that when someone holds a belief in capital punishment, there is a good chance they also have parallel beliefs that rationalize capital punishment as a functional part of that racist system.
In that case, such advocacy is part of their rhetorical framework of hate speech. The clarity of the definition of hate speech gives us to see the context of that.
