I think this can actually be a good tactic. If someone thinks of something like games as entirely good or bad, they will never understand the argument. Many people love alcohol but know it’s bad for them. Many people love games but know that digital restrictions work against them. It’s probably the easiest example to onboard people to the FSF’s ideas because the restrictions on games are so apparent.
I use plenty of proprietary software, but I also know it’s bad for me. Like someone who enjoys alcohol, I think the benefits are worth the negative effects, but whenever I can get the same benefits from free software, I prefer them. I keep one computer around that runs only free software, and it’s great. It’s a decade old, but gains on desktop software performance in the last decade have been slow.
Even Stallman gives one reason to use proprietary software: to make a free version of it. I’ll offer a liberal interpretation of that rule: most people work in technology need to use a wide variety of proprietary software to understand trends and developments in software paradigms, even if they are not directly copying it while using it.
And my prediction: one day, all software will become free. All proprietary software is only temporarily restricted. Future computers will be able to reverse-engineer any existing program and create code that is functionally identical. That still makes it harmful, but that harm will eventually end. We just have the responsibility to make better laws in the future. Most important is preserving political freedom, and software freedom will eventually follow.
I read that more to mean that by playing games that are non-free, you are fueling the existence of more non-free games, and thus doing damage to yourself in the sense of "freedom" since you are perpetuating non-free software. The game itself is not causing harm to you.