Nah, that is Hinduism as seen through the Western lens.

"Sanatana" in Sanatana Dharma means Eternal. The 4 cyclic yugas are well documented in every Sanskrit literature. We are currently in year 5127 of Kali Yug i.e. it started in 3102 BC with the departure of Bhagavan Krishna from earth after Kurukshetra war, which marked the end of previous yuga (Dwapara).

Kali Yug lasts 432,000 years. After which the next cycle begins.

Eventually after Brahma's lifetime is over, Pralaya occurs. Then the universe goes quiet for a long time, until Lord creates again. And this cycle of creation and destruction goes on forever.