I'd be happy to clarify.
Syria has been dominated by the Ba'ath Party, which has a socialist agenda, since 1963. No, the West doesn't not have influence over Syria in the traditional sense, but with the fall of communism in the late 20th century, socialist economies have been drying out. However, know that I think about, Syria used to trade heavily with the Turkey (and the EU to some extent), which are both capitalist-leaning countries.
To my knowledge, capitalism is a Western idea.
I woul strongly recommend reading up on economics, both socialist and capitalist in nature, prior to assigning an 'origin' to one particular idea, as well as assigning blame for Syria's economic difficulties.
I especially recommend this when in your post above, you already noted something which was occuring which was NOT due to 'fault' as has been suggested, by the West.
In very brief form, capitalism is an economic model which has no absolute/precise definition which is agreed upon by everyone. It is however generally agreed that economic activity within the model is in private ownership, is conducted for profit/gain, and that there is competition or the potential for competition.
Due to the competitive and profit-driven nature of a capitalist economic, there is usually more of a free market economic influence than some other economic models will have/allow.
Incidentally, capitalism is generally considered the economic model which replace the feudal economic model in the West. Given that the feudal economic began to be displaced in Europe during the Renaissance and was firmly in place at the start of the Industrial Revolution, capitalism is really no longer a 'Western' idea, since it has literally been around and used for centuries. In point of fact, it was the economic activities in capitalism which are generally credited with allowing the industrialization of much of the world in the past two centuries, and the main economic model followed in the global economy. A case in point would be China (PRC) which follows an essentially capitalist economic model, and I doubt anyone would seriously agree that China is a Western-influenced nation.
Now, socialist economies are a bit different. At a basic level, the methods of production are commonly owned/controlled, and their operation is agreed upon by participants. On a practical level, this common ownership/control and operation really does not work except on small/local levels. For a grander scale, such economies are usually centrally planned and run. Operating an economy in such a fashion has been shown historically to be less efficient than free market economies which do not have (or have less) central control over economic activity.
Now, there are two significant reasons why many of the socialist economies 'dried up' as you put it, after the fall of communism. The first is that with the fall of the Soviet Union, which was arguably the largest socialist/centrally run economy, and the reversion of Russia to an essentially capitalist economic model, there were no longer subsidies available for other similar economies within the Soviet sphere of influence. An excellent example of this would be Cuba, which was/is a communist nation with a socialist economic model. Prior to the breakup of the Soviet Union, Cuba received some subsidies from the Soviet Union, as well as the Soviet Union providing an essentially captive market for some of the Cuban exports like tropical fruits, sugar, etc. With Russia reverting back to a capitalist model, and the use of free market economic activity, Cuba suddenly found itself having to compete in terms of quantity, quality and price when attempting to export things like sugar, bananas, etc. This caused some economic hardship within Cuba, because Cuban goods could not always 'win' in terms of price, quality, etc due to the inefficiencies inherent in the economic model Cuba follows, as well as the fact that economic subsidies stopped.
The second reason is one I already mentioned with respect to Cuba. Following the breakup of the Soviet Union, in order for socialist countries around the world to engage in economic activity, they needed to export goods and materials. However, since the primary markets for such goods and materials had reverted back to capitalist economic activity, the socialist economies were now competing again with economies from around the world to provide whatever was desired. Since central planning (economically at least) has been demonstrated as being less efficient than other methods, those competing socialist economies started to run into difficulty because they seem to have problems being self-sustaining and efficient.
In short, with Syria, after the end of the Cold War, which basically demonstrated that communist/socialist economic models on a macro scale do not work long-term, Syia suddenly found itself needing to participate in the Global economy. Given the socialist economic model being followed, Syria's economy has/had structural issues which has made it more difficult to compete with products/exports from other nations in the global market place. Economically, the world started to change and Syria apparently had a problem keeping up, that is an issue of Syria's not something to be blamed on the West, or the world.
-Cheers