What is the best way for a skinny 17 year old male to gain muscle while not dieting or going to the gym?

You will absolutely not gain muscle if you don't use them. You also won't gain muscle if you don't eat more calories than you burn. I'm not saying go on some diet of salads and chicken breast, but make sure you're eating enough and make sure you get enough protein, that's all. And it's correct that you don't need to go to the gym to add weight, but it's the best way. There are activities that will add mass, like swimming, but you still need to do it enough and do it the right way. Ultimately, you just need to be challenging and overloading your muscles somehow so they adapt and grow.