Yeah, they can all be enjoyed separately. I don't read the comics but other than being in the same universe, the game and show aren't that similar. There are a few characters like Hershel that are in both, but that's about it.
Anyway, check it out. I'd say it's more like Heavy Rain in that it's narrative driven with a few qtes here and there than a straight up point and click, but you do point and click to find out side details and progress the plot at times. It's never a chore though because I find most of the descriptions interesting.