Sorry: 因为主人公是一只猫！

我的理解是：直接翻译就是“如果你触摸我，你就会明白什么是真正的快乐”（因为主人公是一只帽）。如果按意思译我觉得可以翻译成“如果你爱我，就会明白什么是真正的快乐”。

The cats in the musical "Cats" are stray cats, they are "wild". Actions like petting, stroking or cuddling are alien to them because they are something an owner/pet parent would do. So "touch" is actually are more poignant word to use here because it represents the *least* of kind gestures, and that's all that the cat is asking for. An analogy would be if a hungry person sees someone cutting the crust off his sandwich, and he asks him if he can have the discarded crust, not the sandwich. The implication is sadder and more desperate.