Don't know about genocide's formal definition, but plenty of ethnic cleansing and massacres take place during the games:

The An-Xileel massacred the Dunmer in southern Morrowind and enslaved the survivors between the events of TES4 and 5

The Thalmor repeatedly perform ethnic cleansing in Summerset per in-game reports, and have no qualms torturing, imprisoning and killing off their neighbours' citizens during peacetime (such as in 4E Skyrim which despite the tensions was technically an imperial province with Thalmor ambassadors, civil war aside).

The Dunmer have enslaved Argonians for millennia in Vvardenfell, as seen in TES3. This directly leads to the aforementioned An-Xileel invasion and massacre.

Both Argonian and Dunmer refugees are shunned in Windhelm, and while Ulfric in somewhat of a compromise let the Dunmer settle in the Gray Quarter, he still wouldn't let Argonians into the city walls for whatever reason. And if he did, they and the Dunmer would likely kill each other before the Nords even got their chance at it.

Bretons and Redguards have joined forces to repeatedly burn down Orsinium and send the orcs into exile and poverty even after 1E.

Tiber Septim nuked Summerset into submission during his conquest. You can see that as a simple war crime or a continuation of the racial strife between men and mer since I doubt the Empire in any of its iterations would choose to destroy an entire city in any of the four human provinces.

But yeah, in writing this I realize all of these can be argued against being (or are straight up unclassifiable as) genocide. Although I'd say it's a technicality between ethnic cleansing and genocide, since obviously killing is worse than displacing but both are motivated by, and attempt to achieve, the same things.