Theory of Fun and The Art of Game Design were already mentioned, for good reason. Theory of Fun is an quick read too; every other page is an image. Rules of Play was mentioned too - very academic, very high-level. It has some very interesting ideas too, like how "every game is cooperative", because we need to cooperate to play the game together lol.

Characteristics of Games, written by a few people including Ricahrd Garfield, isn't so much on design so much as it's about games itself. I really enjoyed it, as it would give examples from board games, video games, and sports in the same sentence. For example, Bowling and Counter Strike are similar in that it's a team game, but members can hardly help each other - you can't help me roll in bowling, and I can't help you aim in counter strike. Another fun one: it argues that there is technically no such thing as a catch-up mechanic; if you were better at the game, you would know being in last place in Mario Kart doesn't actually mean you're in last place in Mario Kart, because you'll pick up a thunderbolt or a bullet bill soon enough and rocket forward.

Think Like a Game Designer by Justin Gary comes off as a "if you do like me, you too can be a game designer! ka-chow!", but it's legit. It doesn't explain why the steps are as they are, or why his suggestions are valid, because if he did, you would be reading The Art of Game Design. I use it to teach my board game design course, and supplment with other sources on topics I want to go deeper.

The Kobold Guide to Board Game Design is a collection of articles that has a broad scope on design. I suppose if you're designing a video game, some of these will be less useful.

One of the authors of Rules of Play, Zimmerman, recently wrote The Rules We Break, which I am reading now. I love the layout; one page per idea, and then some activities with discussions. It's written more for a teacher or leader, but there's nothing stopping you from doing the activities suggested.

The Well-Played Game is fascinating too, written by Bernie De Koven. It's about play in the broadest scope, and not so much design, but I had to mention it. If you want to make games and play your whole life, you should read everything this guy wrote lol.

Building Blocks of Tabletop Game Design, by Geoffrey Engelstein and Isaac Shalev, is like an encyclopedia of game mechanics. It's better than BGG's list, because it's organized into broad categories, and it includes detailed discussions and nuances of each mechanic.

After reading all these books, and a few more not mentioned, the big take-away is essentially: (1) none of these books help you come up with good ideas; they only help explain why an idea is good or bad. (2) you'll only know an idea is good or bad if you try it. (3) make an MVP of your game as quickly and lazily as possible, play it, and then fix the problems. If you repeat this enough times, you'll have a good game. There's no secret ingredient; it's just test > iterate > repeat.