What's the best way to market my gaming newsletter? I write a little newsletter about gaming over at www.burnthetaverndown.com

Are you a member of gaming communities on social? Or do you have a blog, podcast, or YouTube channel? You can promote your newsletter all those ways at a minimum... also joint ventures with guest expert interviews and the like.

Yes, when individuals are truly enthusiastic about something, it is obvious, and enthusiasm is contagious. Maybe not enough to sell a game by itself, but at least I've learned about different people's independent projects because I was intrigued by how passionately they approached seemingly unrelated subjects.
You can check my blog about this niche here https://collectorpricing.org/rapid-strike-urshifu-vmax-card/298

Interesting 

What about stuff like Discord and Twitch? I'd definitely get in touch with other creators in your niche and do cross promos and things like that.  Especially if you sell merch.