Final answer:
A non-religious semi-subterranean structure similar to ones used by ancient cultures could be referred to as a kiva, an integral part of Ancient Puebloan architecture with ceremonial significance.
Step-by-step explanation:
A non-religious semi-subterranean structure can refer to a kiva, which although historically serving spiritual purposes for Pueblo peoples, is not necessarily tied to any modern religious practice and could be seen in a non-religious context as an example of ancient architecture. The description offered alludes to various types of subterranean structures, such as the spelaea used in ancient Mithraic rituals, and subterranean structures adapted for sacred purposes, like Christian house churches or reused secular spaces. However, the kiva, specifically, is a hallmarked structure of the Anasazi, or Ancient Puebloan people, which was ceremonial in nature and featured a sipapu, symbolizing the place where their ancestors emerged. Remarkably, kivas were not merely spiritual; they had social and communal relevance representing intricate aspects of Puebloan culture.