1. How might different competitive strategies help to explain why Electronic Arts lost its leadership in the video-game market to Activision Blizzard?

Hello, thanks for your question on competitive strategies that might have helped to propel Activision Blizzard past Electronic Arts, as leaders in the gaming industry.
Background
According to newzoo’s 2017 list of top video game companies by revenues, Activision Blizzard ranks third with total (Q1 and Q2) revenues of $3357 Million. Electronic Arts (EA) rank sixth with total revenues (Q1 and Q2) of $2976 Million.
Findings
According to Investopedia, the fact that EA does not totally control its properties, due to licensing partnerships (e.g., the EA Sports and FIFA licensing agreement, NFL), as opposed to Activision, who singly owns most of their important franchises, works to its disadvantage.
Also while previously EA appeared to be more dominant in the mobile gaming category with its acquisition of PopCap Games in 2011, Activision countered this with the acquisition of King Digital in 2015. Through this acquisition, it can tap long-term revenues brought on by King’s games such as Candy Crush Saga and its expertise in mobile game production, especially with projections showing a growth in the mobile gaming industry of about $15.6 billion between the year 2016 and 2019.
Chris Holt, in his article “6 Reasons why Activision Blizzard will Beat Zynga and Electronic Arts” articulates the following factors that might have encouraged Activision’s growth past EA:

Early use of subscriptions: Started using the Massive Multiplayer Online (MMO) in the beginning of the 21st century. It is important to note that the most profitable subscription game for 2016 was Activision’s World of Warcraft (via the Legion expansion). Legion lifted subscriber numbers to 10 Million, with 3.3 Million copies sold before its launch. Against this backdrop, Activision has a large knowledge base on offerings, which it can use to produce similar successful products in the future.

Games have a longer life cycle


Owner of big games that can be further monetized


I hope this helps.