Non-orthogonal multiple access (NOMA) in satellite communication (SATCOM) system can bring high spectral efficiency and massive connectivity. In this paper, we investigate files delivery and share optimization in LEO satellite-terrestrial integrated networks (STINs). A NOMA based coalition formation game (CFG) approach is proposed for minimizing total cost, in which satellite transfer files to head users in each group via NOMA, and head users utilize device to device (D2D) communications to share files among users. Firstly, head users selection algorithm is proposed to choose each group's head users receiving files from satellite. Precoding vectors and transmit power optimization with imperfect channel state information (CSI) are derived to achieve successful NOMA transmission and files download cost minimization in each group. A graph theory based algorithm is proposed to find the optimal D2D links and minimize files share cost. Then, we formulate a CFG and propose a preference order (Group-Best order) for user grouping. Furthermore, we have proved that the CFG with Group-Best order is an exact potential game (EPG), which can get stable group partition and achieve global optimization, i.e., minimizing total cost. Finally, a best response algorithm for NOMA based CFG (NCFG) is proposed to find stable group partition. Simulation results verify that our proposed approach is better than other approaches.