For me, I think it was because it was something different, with so many individual game show elements that sucked you in. Plus, it was definitely ahead of it's time.
From the host (I always loved watching Tom Kennedy shows in the 70s) to the music, the set, the comic book feel to it all, and most importantly, the rapid-fire pace the show went when the clock was running. I can't think of too many other shows from that time frame that had used all of those elements together in one show.
3 years after Whew, there were two other shows that came out that were just as alluring as they had a lot of the collective Whew elements (mentioned above) in their shows: Hit Man (another Jay Wolpert convoluted show) and Press Your Luck, which also had a cult following.
Maybe Whew, like some of the classic cartoons airing on TV at that time, were designed to be entertainment for both kiddos and for adults, but for totally different reasons. I could care less about the questions, strategies and inside jokes when I watched it as a kid. But now that I am watching it 40-odd years later, I'm watching the shows in a different light and am seeing things that completely went over my head back then.
Another show that I think has achieved cult status is The Big Showdown, which also had gameplay and strategy that no other game has replicated...and should.