You can just jump into it.
There are a couple characters that appear in both the game and the series (and I presume the comics, which I haven't read), but they don't have very large roles in the game. Also the protagonist in the game is meeting those characters before the main protagonist in the series does, so at best you are just getting a glimpse of a little bit of their backstory in the game. The game also primarily focuses on characters that aren't in the series.
Also there aren't really any big series spoilers in the game. The only one is perhaps the causes of someone becoming a zombie, but that reveal isn't really that big of a deal.
You can watch the series and play the game in any order (or simulataneously) without either one spoiling or ruining the other. They are pretty much seperate character stories in the same universe.
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