Webster's defines genocide as:
The deliberate and systematic destruction of a racial, political, or cultural group.
Shepard did not engage in genocide. He did not intend for the Geth or for EDI to perish as the result of his decision to destroy the Reapers. The only other two options both required Shepard to trust the Catalyst.
Such trust was necessary to believe that the Catalyst was not lying to him about either control or synthesis and that the Catalyst would not use either to backdoor Shepard. We know that the AI is insane from it's statements and from the statements of Leviathan. We know that it is still hostile because it admits that it controls the Reapers and initiated the Reapers as its solution to its prime directive, but yet it does not call off the Reapers when it admits that its solution is no longer tenable.
Therefore, the continuation of slaughter across the board is used to force Shepard to action. Further, the AI has been trying to kill Shepard for the past 2.5 years and according to the Catalyst the Crucible is not much more than a giant battery. The Catalyst claims that life is preserved, but I submit that he no more preserves life by reducing it down to its elemental DNA than water is preserved by reducing it down to oxygen and hydrogen and storing the gasses.
Where is the basis for trust? There is none.
This leaves destroy as the only viable option. Destroy offers certainty that the Reaper threat will be ended, the AI will be taken care of, and that the slaughter will in fact stop. The cost of this choice is the consequential destruction of the Geth, EDI, and Shepard. Had that choice included my LI, humanity, and myself I still would have chosen destroy and that would not have created a genocide any more than my killing of the Geth was a genocide. Why did EDI and the Geth have to die? Because their intelligence was predicated upon Reaper code.
Was it murder? I think that it was. Shepard caused the death of his friend EDI, he caused the death of another friend's people, the Geth. Did he hatch some plot to systematically erase them from the fabric of the universe? Hardly. Was it wrong? I don't believe that it was. At least it was no more wrong than killing 300K plus Batarians in Arrival.
As a student of ethics, I can find no wrong in Shepard's actions if he picks destroy. There is no basis of trust for control or synthesis and synthesis is a nightmare from an ethical perspective. That said, there is no rational basis to choose either control or synthesis because you cannot say that you trust the Catalyst unless you metagame it. Therefore, the only remaining option from a trust and ethical perspective is destroy even when you include the deaths of EDI and the Geth.
At worst, one can accuse Shepard of justifiable murder, but that is about all you can muster from a rational perspective. Would I have been happier if I could have just taken out the Reapers and myself and left the Geth and EDI alone? Absolutely, but that wasn't part of the deal. Wringing your hands and moaning about the universe being unfair won't change the facts.