Adding the -ing turns the verb "tease" into a noun form that functions as an adjective. "Kittens tease a ball of string." is a full sentence. "Kittens teasing a ball of string" is the subject in the first sentence. "Kittens" is the primary noun and "teasing a ball of string" modifies it. You could also add a prepositional phrase to modify "kittens" as in "Kittens that tease a ball of string." The sentence as you've rewritten it has two verbs. It is grammatically correct and has no clear alternative meaning.

To answer you in the most simple way possible, Pedram: We need to use the gerund (teas-ING) because it is an action that those kittens are doing at that very moment. Whilst they are doing this action (continuously) they are not happy. I hope that this helps. Another example would be: Kittens that tease balls of string do not have fun. This makes it a statement about all kittens at any time. Tom

Thank you so much, Merlyn. Your offering way is so useful.

. the verb in this sentence is "to have" not "to tease" . the phrase "teasing a ball of string" is a adjective phrase .Adjectival verbs are always in continuous (-ing) form. Look at it this way: "Kittens ( who are in the act of ) teasing a ball of string are not just having fun." "Kittens ( when in the act of ) teasing a ball of string are not just having fun." This is a case where the verb to tease must become a verbal noun or gerund. and thinking of it as 'the act of" can help tou decide when to use it.