And indeed there's an important tenet of game design, which I think is found in one of the essays in The Kobold Guide To Game Design: Make the most fun things to do also the things that will help you win. One key thing to do in playtesting is find the strategies equivalent to your "archer spam" example and rebalance so they're not so powerful. It's interesting as a designer to see what players find fun, and vital to test enough that you can empathize those parts.
(Relatedly, one of the pieces of feedback I kept getting on my game Steam Works is that people have lots of fun even if they don't win. That's also a great trait for a game to have but it's rather harder to consistently achieve.)
Plenty of people find fun in very different ways. Some will be happy to play the same simple Magic deck over and over 100 times, not learning anything after the first few plays, and if they win 60 of those they'll have fun. There's a pretty good online survey called the Gamer Motivation Survey by Quantic Foundry which asks you a bunch of questions about what motivates you to keep playing. For example, I get the highest score for Mastery (broken down into Challenge and Strategy), closely followed by Creativity (Discovery and Design). But other gamers will get very little fulfilment from Creativity and much more from Immersion (Story or Escapism) or Social (Community or Competition).
Have you ever seen non-gamers playing a game like Apples to Apples? They're not learning anything or challenging anyone, they've forgotten the score system if they ever knew it, they're just enjoying watching their friends try to work out whether Whipped Cream or Spam is more Cuddly.