Natural gas hydrate (NGH) is an outstanding alternative to conventional energy due to its cleanliness and excellent energy density. However, there are still a series of problems needed to be solved before the commercial production of hydrates is realized, one of which is wellbore integrity. Different from the traditional fossil energy wellbore, the integrity degradation of hydrate wellbore has obvious man-machine and complex system characteristics. Hence, NGH production wellbore barrier classification is defined firstly, as well as failure level and consequence judgment. The system-theoretic accident model and process (STAMP) and system-theoretic process analysis (STPA) methods are applied to establish a hierarchical control and closed-loop model of the NGH production wellbore system. Through inappropriate integrity control actions (ICAs) analysis, well integrity engineers play a leading role in the control loop, and a comprehensive monitoring network helps engineers make effective decisions. Game theory is utilized to study the senior superintendent's supervision strategy and the oil service company's investment strategy for wellbore integrity management selection preference in the test production cycle. The results show that the strategic preference of the executor is related to the frequency of maintenance and supervision, and basically does not change during the production cycle. The growth rate of policy preference value for supervisor decreases with the increase of ratio of partial strategy, but it does not affect the initial preference value. The findings of this study can provide support for wellbore integrity management during test or commercial production of offshore hydrates.