Part of the charm of electronic sports is that no one knows how to spell or capitalise its abbreviation.
There is no conventional way, and no authority to mandate a way.
So… esports or Esports or ESports or eSports or E-Sports or… well, you get the idea.
I think that, intentionally or not, ESPORTS EDITION has clarified everything, as indicated by their “About Us” statement on every page of their website:
“Here at Esports Edition we care only about bringing you the latest and greatest news specifically related to, you guessed it, eSports.”
“You guessed it” is right.
So, keep guessing.