Historically, the white genocide is used by the Armenian diaspora to refer to the threat of losing their culture following the Armenian Genocide. As they moved into new countries, learned new languages and new ways, and married into outside groups, the Armenian culture began to disappear. This was not a 'red genocide', born of blood and violence, but a quiet and persistent loss of culture, a 'white genocide'.
It should be noted at this point that while the term 'white genocide' is the commonly accepted English translation, genocide would normally be referred to as tseghasbanutiun in Armenian, while the white genocide is referred to by other less dramatic names, such as medz yeghern, meaning 'great crime', or spitak jard, the 'white fracturing'.
Fast forward to today. American (and some European) conservatives have taken to using this term to refer to the growing influx of immigrants. Mass immigration has recently become a big issue in Europe, and Americans have been under attack by Mexicans and Jews for decades. There is a definite possibility that the assimilation of these foreign peoples and their heathen cultures will cause the Aryan majesty of the white race to slowly decay and turn a muddy brown.
And so they fight.
No, really, this is a thing. It was apparently kicked off by segregationist Robert Whitaker, who in 2006 published a tract known as The Mantra. The phrase white genocide has been floating around in white supremacist groups (and among other defenders of white culture) ever since. It has come into the US news cycle first with Frazier Glenn Miller's 2014 shooting spree in which he killed three people in the name of preventing such a genocide, and boosted again in 2015 with many white interest groups becoming more vocal in the wake of South Carolina's decision to remove the confederate flag from the grounds of the state capitol.
As you might expect, the movement is well populated with nuts. The official US government petition site, We The People, has petitions like Ask Donald Trump: "Mr. Trump, can you uncuck yourself enough to help us fight White Genocide?" and Investigate why Vester Flanagan wasn't informed that White Genocide is supposed to be carried out non-violently. But there are less discombobulated people with the rhetorical skills to present this as a more serious issue. Maybe.
The White Genocide Project (confusingly, they are against a white genocide) spends quite a lot of effort in documenting news stories from around the world, from Canada to Croatia to Australia, in which white people are being forced to interact with
colored non-white non-Christian non-English-Speaking different people. This isn't exactly Americans projecting their issues onto the rest of the world -- the rest of the world is plenty bigoted without America's help -- but it does seem to be a case of America trying to force American terminology onto the rest of the world.
In the meantime, English is the de facto international language, McDonald's is present in 119 countries, and Christianity is the world's largest religion, with about 2.1 billion followers.