It’s important to understand why sports can increase height. For example, boxing is good for increasing height. Not the part where you get hit in the chin but the part where you are for example shadow boxing.
First, hypoxia is good for increasing stem cell proliferation and differentiation. Hypoxia also enhances expression of Sox9 which is an essential gene for chondrogenesis. A round on the heavy bag is good for inducing hypoxia in your entire body. If you are in development enhancing expression of Sox9 and having more stem cells is very good. If you are not currently growing then you can grow by getting mesenchymal stem cells into the hyaline cartilage in the bone(known as the growth plate line and they’ve managed to turn hyaline cartilage into a growth plate using chondrocarsanoma).
Second, shadow boxing is good for causing shearing forces on the periosteum of the spine and pelvic bones. Irregular bones are completely covered by periosteum so an increase in it’s width by for example shearing forces will increase your height.
Another good sport for increasing height is swimming. Swimming is again excellent for inducing hypoxia and causes shearing forces on your irregular bones in strokes such as freestyle.
These two sports are not sufficient for increasing your height. You also need something to cause trabecular micro-fractures in your short and irregular bones to release red bone marrow which contains stem cells which proceed to differentiate into osteoblasts that then deposit new bone beneath the periosteum which will increase your height. Jumping is one way to achieve these micro-fractures (or rather I should say landing). Long jumping is one possible sport that mimics this or getting tackled in football.
For the long bones, you have to cause trabecular microfractures to release stem cells and you have to load the articular cartilage to enhance chondrogenic expression factors plus load the bones to transport the mesenchymal stem cells into the hyaline cartilage growth plate line. There is no current sport that does this but you can just place a dumbbell on the epiphysis of your long bones.
If you want to increase your height, their are ways to incorporate sports into your height gain routine but you have to supplement that with specific exercises.