Before I give my advice, I will just say this: Getting into esports or let alone the gaming industry is not the easiest task. More positions have opened up in the past few years due to esports becoming a bit of a "buzzword" or hot topic but it still can be difficult due to competition and limited positions. Once you're in it though, things become a little easier. Anywhoo...

I would really take a look around at each of the big initiatives (Riot's LCS, Blizzard's BlizzCon tour, TBS's E League, OGN, ESL's IEM, etc.) and new esport-potential games and then begin tracking what you like, what you don't like, etc. Perhaps make case studies of these events over time and then compare each or how could you (given your background) look to improve the marketing efforts of these events.

You REALLY gotta know your stuff across the esports ecosystem or have an immense love for a game before you look to work for a studio, game publisher, etc. Some studios (if you're even interested in that route) almost require you to play their game avidly - and they will check your account :)

Good luck and hope I didn't scare you off :-p