No. This Table is very much a distortion a truth.  I will take them point by point.

 1. Concept.  The Title 'Who controls your mind' starts from a faulty assumption.  I don't care what is under the at title, the answer will always be 'Me'.  Just because a person or company creates a product, is does not mean that I am forced to consume that product.  And supposing that I actually consume an entertainment/information product that they produce does it mean that they control my mind. No.  The makers of this table lack a fundamental understanding of individual free agency.  Freedom of thought is one of the ultimate freedoms, because it can never be taken from you*. Unfortunately so many give it up so freely.  See [account][1] from Natan Sharansky, a Jew imprisoned by the Soviets for 'Zionist' activities below for example:
>I remember how I loved to tell to my interrogators anti-Soviet jokes, because there were many anti-Soviet jokes, which, of course, were all underground, and telling them openly. And they're so funny that you are laughing. They would almost explode from desire to laugh, but they could not, they had to be angry. They had to show one another how loyal they were. And you're laughing, and so you say, "You see, you are saying to me that you are free and I am a prisoner. You can't even afford to laugh when you want to laugh! So you're the real prisoner." And all the time, it was giving you the opportunity to enjoy the absurdity of this KGB world, and of course it helped a lot to survive in that world. 

 2. Market Share - A select group of companies are shown across various markets, but the complete market is not shown.  For example Google is shown to apparently represent search engines, but absent is Microsoft (Bing), Yahoo, or any other competitors.  Google Search Engine Market Share is approximately [71%][2].  This seems to be the sector that most supports the question, if we look at cable news, of course, it is the opposite, with about [48%][3] of the market being represented by Companies with officers that are Jewish or of Jewish descent.  These two are the easiest to estimate from the chart, since it is incomplete and the market breakdown is not really specified.  

 3. Assuming Jews or Individuals with Jewish Heritage/Culture were officers in News and Entertainment companies, does that mean they control the American media?  The answer is also no.  Similar in part 1, the question derives from a misunderstanding of freedom and capitalism.  Under this system, neither the producer or the consumer completely controls the market, if the producer tries to produce something that does not meet the demands of the consumers, they are quickly replaced by one that does.  Perhaps one could argue that Radio or Cable television are hardly free markets due to FCC regulations, but this list also contains movie, internet, newspaper and magazine companies, which hold no such regulations. Holding a position of power in a company does not allow you to change the market demands, just to influence business decisions in the company.  These decisions may have an impact on market share, but as long as the market is free, that impact on market share is the result of meeting or not meeting the customers demands.  A famous example of this is the [Decline of Schlitz beer][4] from a market leader in the 50s and 60s to a cautionary tale in the late 70s as a result of cutting quality to increase profitability.  This Excerpt from page 89 of [The U.S. Brewing Industry Data][5] exemplifies how efficiently the market can react to changes in a product
>The Company's strategy of cutting brewing costs at the expense of quality and product image also appears in the handling of it's Primo brand in Hawaii.  In the early 1970's Schlitz discontinued brewing Primo in Hawaii and began brewing wort for Primo in Los Angeles, the wort was then dehydrated, fermented, aged, and packaged.  Islanders claimed that Primo's taste had been altered, and its market share in the state of Hawaii plunged from 70 percent to 20 percent between 1971 and 1975.  

F.A. Hayek, a Nobel Economist who studied self Organization in Economic Systems, had an observation in his book, [The Fatal Conceit][6] that I think explains why Nazis have a tenancy to find Jewish Conspiracies like these.
>The result is that such persons (intellectuals hostile to market self organization) are tempted to interpret more complex structures animistically as the result of design, and to suspect some secret and dishonest manipulation - some conspiracy, as of a dominant `class' – behind ` designs' whose designers are nowhere to be found. This in turn helps to reinforce their initial reluctance to relinquish control of their own products in a market order. For intellectuals generally, the feeling of being mere tools of concealed, even if impersonal, market forces appears almost as a personal humiliation.

*This argument does not require belief in the existence of Free Agency (I do, but apparently discussions of free agency are outside the scope of the skeptics SE).  Consider this.  Even if some external force is controlling Natan Sharansky thoughts (as suggested by Christian, Daniel Dannett, and perhaps many others), the fact that he believes he is in control of his thoughts allows him considerable freedom from the attempts of the Soviets at controlling his thoughts by wielding their physical power and controlling the consequences of his choices to the extent they are able.  This is evidenced by the provided reference.  I don't think that I will ever be able to prove the existence of free agency to someone that does not believe it, and is unwilling to experiment with it, but there are plenty of cases, such as this one, that demonstrate that at a minimum a belief in free agency and exercise of such agency can protect oneself from external attempts at control.

  [1]: http://globetrotter.berkeley.edu/people4/Sharansky/sharansky-con3.html
  [2]: http://www.netmarketshare.com/search-engine-market-share.aspx?qprid=4&qpcustomd=0
  [3]: http://stateofthemedia.org/2012/cable-cnn-ends-its-ratings-slide-fox-falls-again/
  [4]: http://www.beerconnoisseur.com/the-fall-of-schlitz
  [5]: http://books.google.com/books?id=C0KUJ0F3XB4C&pg=PA89&lpg=PA89&dq=market%20share%20beer%20schlitz&source=bl&ots=2d25x5lfDb&sig=LV920YNKe7I1v6-_xxsNpUpp-gs&hl=en&sa=X&ei=16YxU47LKKeA2gWug4DQCQ&ved=0CHcQ6AEwDA#v=onepage&q=market%20share%20beer%20schlitz&f=false
  [6]: http://www.libertarianismo.org/livros/fahtfc.pdf