A complex game situation among territorial spatial functions has emerged due to the various forms and unequal spatial distribution of these functions, as well as the characteristics influenced by human demands. To achieve the high-quality development of territorial space, it is important to understand the evolutionary game process and influencing factors of territorial spatial functions. A national assessment is necessary to address these issues, but there is a lack of such research due to the high data requirements. Given this, this research takes 2844 county units in China as an example and quantitatively evaluates the evolutionary game process of territorial spatial functions from 1980 to 2020 based on multi-source geospatial data. Then, an optimal parameters-based geographical detector (OPGD) model was applied to identify the influencing factors of the evolutionary game process of territorial spatial functions. The main findings include the following: (1) During the study period, the dominant game type of territorial spatial functions at country level in China was a positive-sum game, and the game intensity showed an inverted “U” change, with 2000–2010 being a turning period for the game type and the game intensity. (2) The evolutionary game process of territorial spatial functions was dominated by low-intensity positive-sum games. However, there were notable disparities between the two sides of the Hu Line in the evolutionary game process of territorial spatial functions. Specifically, the region east of the Hu Line had a high level of urbanization, a high game intensity, and strong conflict over territorial spatial functions, manifested as a zero-sum game at the expense of agricultural space. The region west of the Hu Line had the widest distribution of game type and conflict type between territorial spatial functions, but the game intensity was low. And the region along the Hu Line was the most variable region of game type and game intensity, and the region with the highest degree of synergistic development of territorial spatial functions. (3) The evolutionary game process of territorial spatial functions at the country level in China was influenced by the integrated effects of natural environment, economic dynamics, and social development factors. On both sides of the Hu Line, the primary factors influencing the evolutionary game process of territorial spatial functions were largely the same. Nevertheless, their role varied, with social development factors having the biggest impact. These findings can provide effective information for achieving high-quality development of territorial space and regional sustainable development.