The example is ungrammatical. Ignore the AI-generated text from the other responder. The text contains obvious errors such as "It serves as a complement to the noun "disappearing."

The clause "that without their activity we could not conceive life" is functioning as a noun complement in this sentence. A subject complement typically renames or describes the subject of the sentence. In this case, "that without their activity" doesn't directly rename or describe "other animals," which is the subject of the sentence. Instead, this clause provides essential information about the situation regarding the disappearance of other animals. It serves as a complement to the noun "disappearing," indicating a condition or circumstance related to the disappearance. So, it functions as a noun complement. Furthermore, you are correct that it's not simply a relative pronoun clause because it's not just providing additional information about the noun "animals"; it's providing crucial information about the circumstances surrounding their disappearance.