Is gaming more addictive than watching movies or tv shows? Are there studies that demonstrate that gaming is more addictive than watching movies or tv shows?

There's this article that talks about dopamine and rewards. It makes sense, but are there similar studies? Any involving tv shows instead of movies?
To answer your question directly, there are so much different factors involved in addiction to games and movies, that I don't believe any study could cover the whole thing. We can, though, try to identify the factors that are different and study them individually.

The fundamental difference between movies/series and games, the one thing that separates more these types of entertainment than anything else, is the following:


  "Mechanics in games imply the need for the player as an active part of the whole system, instead of a mere spectator"
  https://lakitusdevcartridge.wordpress.com/2012/07/05/the-elements-of-game-design/


Engagement

Some factors involve personalizing your character, items and environment. Since people value more to the things they themselves made, they attach to the part of the game that has been designed for them (their characters, their items, etc). It makes them a whole lot more engaged in the process. Providing some personalization to the customer has been used a lot in marketing in order, for example, to sell cake mixes.


  "When we talk to people who bake with mixes, they consider themselves every bit the scratch baker as someone who doesn’t use a mix,"
  http://www.nytimes.com/2011/05/11/business/media/11adco.html?_r=0
  
  "This decorating obsession sold the idea that, this way, you’re making this cake yours."
  http://www.bonappetit.com/entertaining-style/pop-culture/article/cake-mix-history


This type of incentive cannot be applied to movies or series, since the spectator cannot have an effect on the outcome of the scenario. He's a passive observator, probably less attached to the outcome as well.

Comparison

For MMO's or games where you can share your scores online, Envy and pride are also big motivators. These are feelings you rarely have while watching a movie, since your experience is the same as everyone else watching the movie. You can have a leader-board that shows you who's best, you can have multiple stats on which people can compare, you can even have purchasable cosmetic items to put on your character and show other people!


  In-game or in-app purchases for cosmetic items and customization options rake in a lot of money, and developers go to great lengths to make sure that players see all the cool stuff that their teammates and opponents have acquired.
  http://www.psychologyofgames.com/2015/10/podcast-8-envy-and-microtransactions/


Other factors

Although I only mentioned a few, there are a lot of other factors that influence addiction and that are distinct from the ones seen in movies or TV series. I don't think there is one answer, but you can develop form there and add to this discussion.

Again, the main difference between the two types of media mentioned in this question is the role of the consumer. In games, it is an active part of the experience, an actor bound to the media by causality. In Movies, it is a passive spectator and does not hold any power to influence the outcome. This is a good starting point in order to study addiction to both forms of entertainment.