Imagine you're a deer. You're prancing along, you get thirsty, you spot a little brook, you put your little deer lips down to the cool clear water... BAM! A f-in bullet rips off part of your head! Your brains are laying on the ground in little bloody pieces! Now I ask ya. Would you give a f- what kind of pants the son of a b- who shot you was wearing? (from the movie My Cousin Vinny)
At the end of the day, exact definitions are not of much importance. You could be killing people for their ethnicity, their intellect, their religion, their political views or just to maintain power. Are all the examples I've linked to unequivocally considered to be "genocide"? No, of course not, at the very least because the descendants of the perpetrators aren't necessarily happy to be called out for what they did. But if you're staring at the end of a gun barrel, I assure you that knowing if its being done as part of a "genocide" won't make the process any more pleasant.
So I'd go with one of the wider definitions of genocide, this one by Martin Shaw:
Genocide is a form of violent social conflict or war, between armed power organizations that aim to destroy civilian social groups and those groups and other actors who resist this destruction. Genocidal action is action in which armed power organizations treat civilian social groups as enemies and aim to destroy their real or putative social power, by means of killing, violence and coercion against individuals whom they regard as members of the groups.
To expand a bit more, here's an interesting comment by @Kevin:
The basic problem with this definition is the word "substantial." Does September 11th count (nearly 3,000 people died)? Or is that not enough people? Where do you draw the line?
Yes, 9/11 could count as a part of an attempted genocide of American people. It didn't go far luckily but that was very much the intention behind the original attacks. The first steps of many historical genocides also had a small number of initial victims. Government authorities were able to quickly put an end to the attacks, so we now refer to 9/11 as a solitary "act of terrorism", rather than a part of a bigger chain of attacks.