Did India and the middle east operate in the feudal way that CK2 depicts Europe as?
In a video game, most things are abstractions rather than direct representations. Hit-points are an abstraction of how wounded a character can be before they are unable to fight, but in real life a bullet is not going to care what your hit-die is.
In this way, the mechanics of Crusader Kings 2 are an abstraction. But to properly answer this, we have to start with the question: What is Feudalism?
This thread discusses the idea better than I ever could:
That being said, if we use the term to refer to the specific idea present in popular culture of land being exchanged for service, reinforced by an identification of the rights and responsibilities of each party, I think that would be an effective, simplified summary.
Here is the problem, that definition can be associated with numerous relationships throughout history with different cultural contexts.
Take for example the Byzantine Themata System from the 7th to the 11th century AD. Byzantine soldiers (Stratiotai) where given land in which to support themselves. Here is a good summary:
"In two texts from the mid-eighth century—a paragraph in the Ecloga of the Isaurians and a court decision attributed to Leo III or Constantine V—we find references to soldiers who were owners or joint owners of land, who bought and maintained their armament from the money produced by their land, and who contributed the salary (roga) they earned when on campaign to the family budget.22 In other words, these were soldiers from rural areas who relied on their landholdings to maintain themselves"
That would fall into the category of land for service, but it was a relationship between a governmental body and a landholder rather than between an independent land-holder and another land-holder. Would that still be feudal?
A similar system would the Iqta' of the Islamic world, which became common the 10th Century AD. A solider was assigned a particular piece of land from which to collect tax and rents. A good explanation and discussion can be found in the book A History of Islamic Societies:
Like the Byzantine Themes, it was based around the idea of land for service, but the soldier only had the right to collect rent. There was no form ownership in the Byzantine sense, nor did the soldier have rights of justice and administration. It was likewise a relationship between the state and individual.
Likewise there were client/patron relationships that lay outside formal legal frameworks, such as the Ancient Roman Clientala:
"The patron was the legal adviser of the cliens; he was the client's guardian and protector, as he was the guardian and protector of his own children; he maintained the client's suit when he was wronged, and defended him when another complained of being wronged by him: in a word, the patron was the guardian of the client's interest, both private and public. The client contributed to the marriage portion of the patron's daughter, if the patron was poor; and to his ransom, or that of his children, if they were taken prisoners; he paid the costs and damages of a suit which the patron lost, and of any penalty in which he was condemned; he bore a part of the patron's expenses incurred by his discharging public duties, or filling the honourable places in the state. Neither party could accuse the other, or bear testimony against the other, or give his vote against the other. The clients accompanied their patroni to war as vassals"
Source: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Cliens.html
The relationship is very similar to the popular conception of European Feudal relationships, but without the classic form of knight/lord.
My point to all of this? There were lots of relationships that, on the surface, were "feudal" in nature but were in actuality quite complex and stemmed from different cultural traditions.
In this way what is presented in Crusader Kings II is basically a broad form of categorization design to distil a large number of legal and social forms of organization into a format than can easily be understood and recognized by a Western audience.
Edit: However, the drawback is that players will come to view all relationships throughout the period in a European-Feudal context, when it was rarely the case at all. This results in a huge amount of misinformation and inaccuracy, meaning it is not correct at all.
CK2 isn't a very good model of feudalism at all, no. Even restricting ourselves to just feudal Europe (which isn't appropriate for much of the time period CK2 now covers even inside Europe):
Speaking of Normandy, appanages are still not a thing in the game. A lot of not-purely-hereditary-or-elective mechanics are not implemented in the game, but appanages are the first that come to mind.
As other posters reference, CK2 runs on the implication that if you make someone a count by giving them land, they suddenly own that land in full. And you can then lose it if someone on another continent ends up inheriting it. This makes about as much sense as a Japanese citizen buying some land in Iowa, and because of this, Japan claims it as part of their sovereign territory. That it takes decades for the war to reclaim it to finish is just icing on the cake.
The 'three estates of the realm' that CK2 runs on is a rather fanciful term, and was never appropriate. Every castle and even church is presented as a major fortification, every city is presented as being comparatively weak defensively. Cities like Rome, Cologne, Uppsala and such were cities first and foremost, not churches. A better division would probably be to divide holdings into rural, urban, and unsettled, and go from there.