This is really easy. The only reason to go to the gym is to get bigger muscles, and you don't want them. They are not necessary for your health. It's always better to play than to just exercise -- frankly, I played until I got too hurt to play anymore and now I exercise, which is dull and I'm still getting hurt. Both sports you play are building muscle as well as giving you great cardio, as they use arms (tennis) and thighs (both). So just eat more. That's all you have to do -- eat more of the healthy food you already eat, maybe add a meal, and you'll gain weight and keep doing what you want to do.
You don't have to go to the gym to do this. You can strength train at home. Weights are pretty inexpensive and you can keep them in your bedroom or living room and work on that in your house. Also, how many days a week do you work out? You wouldn't go to the gym and lift every day. Maybe two to three times a week and the other days you do your outside sports! Also, your own body weight can build strength. Push ups!! Lots of them. Core work, lots of it. Squats. Get some exercise bands and it's like a resistance work out that builds muscle.
You can have the best of both worlds. good luck
Hi, as you've just heard, you have to eat more and do resistance exercise (especially at home). But you'll also discover that you likely just don't have enough recovery ability to do sports regularly and also gain much muscle mass at the same time. If you try anyway, you'd need to throw in extra sleep and also restrict all other movement, which even has a scientific name: NEAT for Non Exercise Activity Thermogenesis.
There's a guy named Martin Berkhan that became rather famous with his "Lean Gains" but I'd say that's mostly misleading. You'll have to gain some bodyfat, unless you progress very very slowly - like maybe a pound a month.
Also btw, you can get somewhat stronger without getting bigger, especially initially (called beginner gains) though you'll hit a plateau on that. The reason is that initially, strength increases mainly from the neuromuscular ability to recruit more muscle fibers in a movement.