Learn English – What does “play games” mean in this sentence

Very simple words like "play" or "run" or "go" have so many meanings that it's often difficult to tell which is the correct one for a given use. In this case, play means to utilize or exploit. From the Merriam-Webster definition:

play (v) 2.a: to take advantage

So in this sentence, the author is stating that extortion hacks work well because they are able to make use of a company's fear of lawsuits, etc.

I'm not sure that I would have chosen play to here though. In a negative sense, it's almost always play on. When someone plays to someone else, they are generally behaving in a way that is calculated to gain favor from the target of the behavior. You might play to an audience of chemists with science jokes. That would be Merriam-Webster verb definition, 3.d, if you're curious. It's possible that the author was trying to use this sense of the verb, but it's not the typical context you would find it in.

In this context, I think the author is simply saying:

they’ll go live recklessly and behave dangerously

The reason we might tell someone to "go play in traffic" when they are annoying us is that we want them to go away and not come back. I think the phrase is used in jest; if taken literally, it's almost like we are saying that we hope they will go get seriously injured. (I'd recommend most learners avoid the go play in traffic idiom.)

Similarly, and eight-ball of cocaine is a pretty large amount (3.5 grams), and according to one website:

The estimated minimal lethal dose of cocaine is 1.2 g, but individuals with hypersensitivity to cocaine have died from as little as 30 mg. Still, this is usually not the case with cocaine addicts, who develop a high tolerance to cocaine in the central nervous system. In fact, some cocaine addicts with considerable tolerance have reported that they can tolerate up to 5 g of cocaine daily.

So, your sentence begins with:

This truth [that everyone will die] will liberate them from all responsibility, and they'll go snort an eight ball of cocaine and play in traffic.

In other words, because they feel like nothing they do will prevent their ultimate, eventual death, they simply won't exercise caution while living. The author could have just as well said:

This truth will liberate them from all responsibility, and they'll go take lethal doses of drugs and do very dangerous recreational activities.

However, that paraphrasing is more bland than the original. I don't think the author is using established idioms per se, but rather simply furnishing some colorful examples.