I dont know of anyone pushing a communist/socialist revolution and pushing one for a "globalist" agenda doesnt make much sense. Most Communists and Socialists are not fans of globalism.
You make a fair point, it's my fault since my answer was severely over-simplified.
I'll try like this through the class system :
The 'elites' (Superwealthy, internationalists, royalty, world leaders in their fields) : Because of their intertwining and interdependant relationships and influences control the vast majority of the economies, cultures, etc of those beneath them. These are the people that are the TRUE globalists, that have a disdain for humanity and have a desire to consolidate their wealth and power into a singular world system that would serve them at the expense of everyone else, regardless of their stated political beliefs.
Because the elites have MORE WEALTH then they could EVER spend even if they tried they enjoy an existance beyond the day to day concerns of the majority of the rest of the populations. Because they are humans already with great power, they are following their human nature to put their efforts into expanding that power... and they do so by 'colluding' (over the table and under the table agreements) with others of similar status. Individually, they are merely interested in protecting their power so that their children will be as powerful into perpetuity.
THESE are the pushers of the 'new world order'. You won't find them pushing for this in the mainstream media (untill relatively recently), but rather will find their intention in books that they write, white papers, and other documentation which is not 'classified', but neither publicized.
The wealthy classes : This is the group where you will most likely find proponents of the benefits a global government would offer (fewer wars, every individual fed, clothed and housed, etc). there are also those that are wealthy that have or had the intention of changing the system once they become / became wealthy, but then lose that passion once they get all the benefits of the system they were previously fighting. This group has the most to lose by speaking out against the system... 'don't bite the hand that feeds'.
In the end, the majority of the 'good intentions' of the wealthy end up corrupted by the elites pulling the strings above their heads.
The middle classes : We are essentiall pawns in this global power game. Kept in a rat race where we are envious of those that succeed and try to replicate that success for fear of failing and joining ranks among the poorest. We are kept controlled through a variety of means : sports (to feed mans tribal nature and to spend energy that might otherwise be directed politically), the media (to send the message that individuals are 'powerless', to trust 'experts', and how to become good 'consumers'), fluoridated water (to render the people more passive OR excessively aggressive, since different people will have different reactions to the fluoride), pharmaceuticals / illicit drugs (because addicts are easily controlled), food (because you can't overthrow a government on an empty stomach).
The poor : This group is the motivating factor for the middle class, but are rendered politically impotent because so much of their energy is spent on day-to-day concerns and survival rather then things like debating the politics of their country.
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My use of 'communist / socialist' was also somewhat inaccurate because the 'new world order' is meant to be neither of those things, though it would resemble them. I mainly used that term because those systems generally revolve around a centralised governmental system rather then a representative one.