Legally and conceptually animal crueltly doesn't just mean "painful or deadly things happening to animals. Despite the name it is more implicitly "gratitutousness animal cruelty" which is defined as not serving a purpose.

Tar paper traps lead to a slow death by starvation but it is a side effect of the function - to work without "triggering" and inconveniencing anything much larger instead of risking harm. No need to take a cat to the vet if they step on it, just wash them off and maybe clip some fur keeping it attached. The fact it causes more suffering than a mechanical trap isn't enough to qualify although one may object to its usage. But breaking a mouse's leg just to laugh at it and watch it crawl? Gratitutous and would qualify as animal cruelty.