There's no right approach
There’s no one right way to implement esports. As you proceed with your esports program, gauge your capacity and comfort and start from there. You might prefer to integrate competitive esports experiences into your classroom to meet curricular expectations. Or you and other interested faculty may decide you have the capacity to offer a larger extracurricular experience.
You may also find that labeling it as an "esports" experience may seem intimidating to some students, so you can also label it as a Minecraft, or gaming club, and gradually integrate competitive experiences.
The important thing is promoting fun and future-ready skills!