IF you desire to attach this definition of "group" to a...

IF you desire to attach this definition of "group" to a genocidal terrorist group (Hamas) then yes it may suit.
The problem however is that you and the world screaming the term are NOT using it for this. (There is ZERO intent to harm innocents).
If you believe that Hamas should remain with their members openly calling for the murder of Jews and absolute destruction of Israel (with their continued actions consistently proving such aim) then you are a supporter of terror and genocide.