America is around 70% white, Canada with the smaller population is about 75%-80% white. half of the hispanic population is white thats half of 16% which is 8%. 70 + 8 = around 80%. Also, the majority of goverment, media and ruling class are white.
South America population is 40% white meaning they are the single biggest race in South America, every other racial category is lower which makes whites technically the majority, you don't have to be over 50% of a population to be a majority. Roughly 30% of the south american pop is either mestizo or mulatto, meaning they are at least half white. So 40% of South American population is pure white and at least 70% are either full white or half.
Middle Easterners are nearly 100% caucasians, religion has no correlation with race. White is a race not a religion, if John Smith from Nebraska became a muslim tommorow doesn't mean he's not white anymore. A good number of middle easterners are physically indistinguishable from whites, including different hair and eye colors. If a Filipino, a Japanese and a Thai person can all be considered under the racial caetgory of "Asian" then Middle Easterners can be classified as white.
Whites inhabited the richest and most diverse lands on the planet: North and South America, and Australia, these are new continents, which were mostly unminned, untapped and overlowing with natural resources. The population density of white countries are lower thats why they have lower populations not due to any lack of land or resources, its nobodies fault but theirs that they don't want to make more babies.
I agree mostly with your post except for the middle east. Culture plays a role in defining a race and whites are basically people with european heritage, both genetically and culturally. I know middle easterners and even indians can be considered caucasian but they're hardly white. There are exceptions though. It's not because of Islam, Albanians are white, but Saudis not really. You can make exceptions for some iranians, pashtuns and so on who at least speak an Indo-European language. But whatever.
Some very rough math:
200 million whites in the US
50 million whites in Brazil(debatable, the census give double these numbers but the large amount of christian arabs and light skinned mixed race are considered white there)
500 million whites in western europe(the EU has 510 million people, no clear race breakdowns, of course there are many non-whites there but western europe also includes other more white countries like switzerland and norway not in the EU)
28 million whites in Canada
25 million whites in Australia and NZ and other small islands
120 million whites in Russia
50 million whites in Belarus and Ukraine
100 million whites everywhere else/probably an underestimation(Argentina, Uruguay, Mexico, other latin american countries, South Africa, expats in China, Saudi Arabia or whatever)
Over 1 billion white people around the world.
There are many more people that are partly/mostly white in Brazil, Mexico, Cuba and the rest of latin america.
For comparison there are 1.3 billion Han Chinese.
1.6B muslims(of course they comprise many ethnicities including white)
Probably around 1B blacks(800 million people in Subsaharan Africa, 35 million African-Americans, 100 million brazilians with some african ancestry although only 14 million identify as pure blacks and genetics confirm most african brazilians are mostly european especially in the paternal lineage)