Personally, I think you should. I played the game back in 2013 though Im not some TLOU purist or someone who thinks its the best game in the world. However, imo, the game is so much better than the show. The show felt rushed at times and instead of seeing Joel and Ellie's relationship develop over time we got a huge time jump and was told "Yeah these two are cool now". I understand that the show had only 9 episodes, but I just didnt feel any of the relationships develop naturally in the show. I think if you play the game you will have a better appreciation of almost all the characters. Plus its a pretty fun game.