There are various terms for both. Bookworms, cinephiles, movie buffs, bibliophiles.
Maybe if it's a "branding" problem, of sorts, using other words would work, like ludophile, but it doesn't avoid the fact there are cores of enthusiasts for most (all?) media.
It's all no-thought, meme-chanting-so-I-feel-like-I-fit-in middle-school behavior. It's the same groupthink of pop Internet culture (reddit/4chan).
Language didn't all of a sudden become silly. Its always been like this. Personally, I love the term gamer as its used, almost exclusively, with the FPS and racing game obsessed manboys I love to hate and go out of my way to avoid.
Normal people tend to say "I play video games" or "I play $whatever." Gamer as a self-identification is very useful socially.
A person can be a "gamer" without having video games be their whole culture and identity, just as they can be a "sports nut" without having their favorite team be their whole culture and identity.
The fact that there's a concise word for "enthusiast in this particular area" doesn't imply anything about gamers that it doesn't also imply about other enthusiasts.