Alpinia hainanensis is a member of the ginger family (Zingiberaceae). This family of plants is characterized by producing underground rhizomes (underground stems). These rhizomes continuously produce new shoots from under the ground as the plant grows. If you would like to transplant some into your garden, you should cut pieces from the underground rhizome. The pieces should be thick and fibrous and will probably have roots and shoots growing out of them. If you look at the ground around the larger plants, you will be able to locate younger shoots coming up. You can remove these younger plants (dig them up with the rhizome) to transplant to your garden. It will not do any permanent damage to the mother plant. The "ginger family" link below offers additional information.
https://en.wikipedia.org/wiki/Zingiberaceae