Maybe a "Lamb Token" is being tributed to allow "Giant Rat" to attack; Both are Beast-type monsters.
The fact that this card's effect doesn't apply to Machines and Zombies maybe is possibly because they aren't "alive."
In that case, it's unknown why this effect isn't also applied to Rock-Type monsters.
However, there are some Rock-Type monsters which are merely animals/fighters with an earth theme (such as "The Rock Spirit" or "Legendary Jujitsu Master") or exceptionally hard skin. Machine monsters were, by their very nature, manufactured, and Zombie monsters are living dead. Thus, these two types can be said to not be "alive" in any traditional sense.