I mentioned this preference to some other fans of the "Walking Dead" games, and one of them recommended TellTale's newer title, "The Wolf Among Us".
I beat episode one in a single sitting, and I have to say, I was not disappointed. In fact, "The Wolf Among Us" might even be better than "The Walking Dead".
From a storytelling standpoint, it is a bit harder to relate to the characters. Pretty much the entire cast (everyone that you interact with at least) is directly pulled from another story. Even one fable, that I could have sworn was written specifically for this game (or the source comic), turns out to be a french fairytale published in 1695. Identifying with a normal person stuck in a survival situation is certainly easier than identifying with a non-human entity who's existed for hundreds of years. Still, the creators did successfully humanize and modernize the characters.
Players of "The Walking Dead" will probably remember a few moments that were unexpectedly cruel, were you witness a characters fate and can simply dwell in the dejection while saying to yourself, "I can't believe that just happened". Similarly, I can think of a few times in this episode that gave me the same feeling. The fact that a video game that emotionally shock you in such a way is actually very impressive.
I highly recommend everyone buy this game. Even after hearing good reviews and positive endorsement via word of mouth, it turned out to be better than I expected. I'm looking forward to the rest of the season, and have already preordered.