Well you can not argue with how the world looks like toady:
African borders were drawn by Europeans.
Different cultures around the world use the European concept of "surname" and "given name"
Most states follow the nationalistic European concept of a state - with a national anthem, a flag, an emblem, a moto, and such.
So you can't argue that in the past ~250 years Europe actually rules the world.
Well, in terms of
culture and
science it is obvious that Western Europe has dominated the world in last... 250 years.

Although last decades see such big contributions of Japanese/Korean/Chinese/Indian science that saying 'science is only in Europe' is definitely not fair.
But saying it
actually rules the world for last 250 years is technically wrong
In terms of actual imperial domination Europe (...including Latin America) was dominating the world approximately between half of 19th and half of 20th century.
On one hand, influence of Europe on Orient:
- law and politics
- modern science
- parts of European culture (tuxedos, golf etc

)
- economic solutions
On another hand, influence of Orient on Europe:
- before 16th century: really many technological and scientific solutions which, along Greek and Arabian science, begun scientific revolution
- pretty huge spiritual, philosophical and religious influences
- parts of Oriental culture (kung fu, oriental arts etc

)
But Indians and other southern/central Asians were brought down quite easily in their first clash with Europeans.
It depends on which country you are talking about
India was brought down because it was extremely fragmented on countless factions which were manipulated by British Empire and falling in its sphere o influence one by one (British also had enormous advantage in global trade and naval tradition).
Afghanistan, on the other hand, completely annihilated the British expedition sent to it - but hey this is Afghanistan
Siam, Persia, Ethiopia, Arabia and Japan managed to avoid colonialism.
China and Ottoman Empire were simply too big for European empires to annex (as you can see, united India rather wouldn't be conquered by British)
Some areas were slowly dominated using various economic or military means (India, Indochina), some were dominated as some kind of semi independent protectorates, some were conquered by military means relatively easily (most of Africa - Zulu are very overrated...) and some were conquered but after strong resistance and heavy European losses (from what I remember,
Ashanti and
Sikh were very hard to conquer by British empire).
Chinese, as much as I know, beside trading, didn't have much political interface with far away cultures, compared to Europeans / western/southern Asians. I might be wrong though.
You are rather right although I wouldn't underrate Chinese trade
And the rest of the world - most of Africa, Native Americans, and most of Central Asian history, are not much of a contest to Europeans...
I definitely wouldn't count Central Asia as not a historical contest to Europe. I mean, of course Europe was more developed, but man when steppe hordes were angry Europe was terrified

If I remember properly, Moscow was last time burned by some Horde in late 16th century
Native Americans had extremely bad luck and much worse geographical conditions. Although world still seems to be impressed by pre - Columbian culture and architecture
Personally I am annoyed by the fact that everyone knows Aztec and Incan empire were massacred by very small force of Europeans, but
for some reason following facts are usually unknown:
1) Epidemies brought by Europeans didn't exactly
weakened Native America as
almost completely annihilated it and Europeans were conquering the ruins of former glory

Come on, show me a civilisation which performs good in war when 93% of its populaton is wiped out by a plague.
2) Aztec Empire was brought down not by 500 Spaniards but
by 500 Spaniards and dozens of thousands of natives allied with them to destroy Aztec regime
3) Incan Empire was indeed conquered by group of Spaniards... During a massive civil war

4) Native Americans weren't dominated by Europeans as much as we tend to assume - it annoys me that while everyone knows about complete fail of Aztec/Inca, only few people know for example about
http://en.wikipedia.org/wiki/Arauco_War
----------------------------
On the other hand, yeah, I have to agree that most of Africa was ages behind Europe Europe. The same with pre - European Canada, Brasil, Australia, Oceania, Siberia and so on. I guess these areas were bad for the rise of civilisations.