Right, that is the official definition of genocide. And note, the intent of the official definition of genocide, is to define genocide. Not to rule on whether or not retaliation is appropriate. So while showing whether or not actions amount to genocide is important, discussing whether retaliation is permissible is irrelevant and tangential.
So let us review, shall we?
Hamas:
Did Hamas....
- Killing members of the group - No. They killed a multi-national, multi-religious, multi-ethnic group of people. No one specific. Infact they explicitly DID NOT intend to target civilians and have admitted that there were some faults that occurred on October 7. Many Israeli survivors also said the same thing, where the Hamas guys let the women and children go.
- Causing serious bodily or mental harm to members of the group. - No. They harmed a multi-national, multi-religious, multi-ethnic group of people. No one specific.
- Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part. - No.
- Imposing measures intended to prevent births within the group. - No
- Forcibly transferring children of the group to another group. - No. Kidnapping does not count as forcible transfer as they did not steal kids to convert them into Palestinians.
Note, that committing only one of these crimes is enough to be genocide as long as, INTENT, is displayed to in whole or in part, destroy a specific group. So did Hamas display that INTENT? No. They did not.