Let me explain the military-entertainment complex to you like you are 5 years old.
You know how you like to play with action figures and watch superhero movies? Well, some grown-ups like to make movies and video games about soldiers and wars. Sometimes they even use real soldiers and military equipment in these movies and games!
Now, these movies and games are made to be entertaining, but they also sometimes help the military recruit new soldiers and make citizens feel good about going to war. This relationship between the military and entertainment industries is called the military-entertainment complex.
So basically, it's like when you pretend to be a superhero and play with your action figures, but grown-ups are doing it with real soldiers and weapons, and sometimes they use it as a way to make people support military actions.