I originally wrote this as a response to Mathel but I tried reworking to address more of the ones with similar points too.
Personally, I always thought of genocide as meaning specifically killing of people based on ethnicity. Similarly to how fratricide means killing one's own brother, regicide means killing of a king, fungicide is something that kills mushrooms, and so on.
Neither of these other "X-cide" words can mean killing of the concept of X (or a specific case of X). So genocide should not mean the killing of the concept of the group, but the actual killing of the group. Which is done by killing it's members.
Genocide, the term, was coined by Raphael Lemkin, a Jew who fled Europe to America, iirc in the 30"s or 40's sometime. He explicitly defines it not just as killing persons but killing the people. Cultural destruction is central to his ideas. In his writings he exemplifies this with the soviet Union Holodomor, the genocide of the Ukrainian people, and how it involved not just the structural starvation of people but also the attempt to stamp out the Ukrainian identity and institutions, the cultural habits which differentiates them from Russians, and their language.
Genocide was a new idea that hadn't really been put into a word before, despite nationalism being an ideological centerepoint for Europe for the last two to three hundred years or so and the idea of the nation state (summed up in one sentence as "one state, one nation") shaping European governents' attitudes to minorities for a whole lot of that time. But the term described something real, and was quickly recognised at least partially, since it's coining came very timely with the need to describe the Holocaust -- their first briad usage iirc was during the Nutnberg trials. Lemkin's ideas met resistance, however, when it came to fully implement them into UN conchords, as while European powers and rhetoric US had been quick to use the parts of the ideas regarding ethnical cleansing theough mass murder to heap blame on Germany over the Holocaust, really did not want to acknowledge the parts about cultural genocide since that would incriminate their own pursuits of the nation state as genocidal. So they cut the ideas up and only legislated the parts of it they liked, and that is why the UN definition of genocide to this day only concerns mass murder.
The thing is, though, that Lemkin's ideas about genocide become hollow and hypocritical if one does not acknowledge the parts about cultural genocide. The idea of genocide do not hold up unless one also acknowledge the idea of the destruction of the genos as a crime against humanity. These are the parts of his ideas that put into thought a new concept, that needed a new word to be described. There already existed plenty of words for massacring and mass murder (Holocaust being one of them), that wasn't anything new. Sequestering genocide to just being about killing persons goes against the very point of Lemkin's ideas and work.
Personally, I always thought of genocide as meaning specifically killing of people based on ethnicity. Similarly to how fratricide means killing one's own brother, regicide means killing of a king, fungicide is something that kills mushrooms, and so on.
Neither of these other "X-cide" words can mean killing of the concept of X (or a specific case of X). So genocide should not mean the killing of the concept of the group, but the actual killing of the group. Which is done by killing it's members.
But I also wanted to respond more directly to this point too. Those other things –the brother, the king, the fungus – are actual things that can die and be killed. A
people, a nation or folk or genos, only exist as a concept. It is an identity. It is a thought. It is conceptual. It can only be "killed" as a metaphor for it's destruction because it is only "alive" as a metaphor for it's existance. That is the difference between these words.