Reminder: KIDS. Kids haven't yet been brainwashed into believing that crawling, or sitting on the floor, or playing make-believe, is undignified. Frankly, I don't find it undignified either, and I haven't been a kid for [mumble] decades.
Of course there are contexts of coercion and the like which would give it a different interpretation. And there are people who can't deal with the concept of an adult -- or a kid -- being only as dignified as is actually appropriate for the situation. But that's like saying that bathing suits are undignified because they expose more skin than would usually be considered appropriate for an audience with the Queen. Context matters tremendously!
If this book is like most of its kind, odds are extremely strong that the game was invented by kids and merely documented/formalized by the adult writers. And this one in particular is probably age-appropriate up to kindergarten or so, if that; after that it's simply not interesting.
So: If it doesn't sound like fun to you, that's fine; don't play it. But heck, I will still play cat on occasion to get a laugh out of friends. And I remember playing this when I was that age and it really did NOT carry any of the connotations you're worried about; it was just a more organized party-game version of the make-each-other-laugh game we already played with friends.
If you can't be silly when you want to be, and can't laugh with your friends when you want to do so, you're doing it wrong. For many values of "it".
(If you're worried about kids being coerced to play a game -- ANY game -- that's a completely different kettle of worms and probably belongs in a different thread.)