Nah, do the books or show. All these telltale games are better knowing the world beforehand

The TV show would be better

TL;DR, for Expanse newcomers, I'd recommend bingeing the show before playing the game.

Do you like science fiction TV shows? If so, then I'd recommend the TV series. Do you prefer to read SF? Then I'd recommend the books. Both are pretty good, though the TV show adaptation made a significant number of (mostly) warranted changes from the books.

I would trust that the game does a solid enough job for newcomers to the series, but you'd likely get more out of it if you'd seen the show. The main character in the game (Drummer) is a prominent side character in the TV show, and I believe the actor for that role is doing the voice over for the game. Which is awesome, she was one of my favorite characters from the show. I believe that character doesn't map one-to-one onto any character in the books though, as the show condensed and combined a number of side characters. I felt that was an understandable change for the TV adaptation since the books had a fairly sprawling cast of side characters. Anyway, long story short, if you're on the fence for book vs. show, I'd say watch the show since the game appears to match the show's continuity.

The game just released today and I haven't played it yet. It's also releasing in episodic fashion, as many Telltale games have done, so you'd only be able to play the first installment today. Reviewers have access to the first three, according to this review-in-progress, but as that reviewer points out:

I've not yet finished all of the episodes, with only the first three available to review, but what I have played is exceedingly promising. At this point, my only question is whether the core mystery is satisfying and if the developers manage to stick the landing, which is impossible to answer without fully understanding the breadth and scope of the entire set of episodes.

I love both the books and the show, and while I'm looking forward to the game I've decided to stay on the fence until all the episodes are available.

Edit to add: IMO the TV show did stick the landing, so I have no reservations about recommending it to anyone. The TV show covers the first six books of the series, and just like in the show book six ends with a pretty satisfying conclusion to the story started in book one. In book seven there's a 30-year time jump, so books 7-8-9 are kind of a separate-but-connected story arc. Books 1-6 I loved, 7-8 I'm lukewarm on, and that's made me less inclined to invest time in book 9 but I probably will at some point.