Hm. The best answer to this question is that the path is unique for everyone. I'd start by working on your prose, and getting your core writing talents up to the level of your tastes. For the actual job path, though? It really, really depends. For instance - (cue flashback music)
I've been writing since about the sixth grade, and started writing professionally about halfway through college. I didn't study Creative Writing, though. At the time I hadn't really liked CW curricula (mostly because it focused on dead white guys writing mean letters to their kids), so I ended up studying political theoretics -- writing comedy sketches and reviews for deep house/techno music on the side (our magazine was extremely popular in the German underground). Eventually I followed the poli sci path to Switzerland, where I studied poverty politics in at the Université de Genève and started doing some financial analyst work in and around the IMF.
International finance was a mistake. I was great with collecting information, but extremely ill-suited to working with numbers and deliberately ignoring the human cost of whatever I was supposed to be working on. I came back to the US, picked up music reviewing again, finished my undergrad degree and moved to LA -- where I landed, somehow, as a games journalist.
Did that for a while (eventually I'd try international finance one last time to disastrous results) before contracting with Pole to Win as a QA on Touch My Katamari. Of my team, I was the only one who knew what the Katamari series was, and one of the longer time employees didn't like me because I wore a puffy blue scarf and ate lunch on the roof. He had seniority. It was... not my favorite position.
Eventually I moved on.
Cue the music industry again. Then talent management. Eventually back to games journalism, and then... well. Something unexpected happened. I was 24.
I chased the youtube rabbit for a few years, but as many of my former collaborators will tell you, that life kind of sucks. At 25 I won an international writing award for journalistic excellence and, in a twist of fate, was terminated from my job for it because ha ha whoops I whistleblew on their awful management and talent practices. An old buddy of mine was talking about the situation to a friend who worked here, and Riot eventually contacted me with an offer... just a scant two months before I would have run out of rent money. Did a brief stint with Cards Against Humanity to help me not starve to death, and then eventually I was here. Not on the writing team per se, but here.
After that I just kept honing my craft. One of the old leads asked me to submit dialogue lines on Ekko, and my major contribution to that was coining the term "Pilties" (thank you Political Theoretics! YOU WERE USEFUL AFTER ALL). I got to keep writing lines while at the same time writing and producing a lot of the cartoons you see on the League Community page (thank you being a mid-level YouTuber! YOU WERE USEFUL AFTER ALL), until, one day, I was offered a slot in the narrative team proper.
So to answer your question of what to do to get a job like this?
Write well, don't stop writing, and network like an axe-wielding sociopath. If you're lucky it'll all work out. Possibly.
Maybe don't listen to the things I say.