An analysis of the evolution law of radical innovation process (RIP) and an identification of the RIP's influencing factors, particularly to solve the low success rates of the radical innovation of high-tech enterprises, is the focus of this study. The dynamic evolution of RIP can be explained from the perspective of market timing of innovation processes. Moreover, the key influencing factors and the impact mechanism of the process of evolution need to be identified. The window of opportunity-evolutionary game theory (WoO-EGT) model of RIP, which was built by combining WoO and EGT, was used to analyze the dynamic evolutions of the RIPs of existing and new high-tech enterprises. The three categories of RIP evolution when WoO was opened-only locking technology, only breakthrough technology, and coexistence of locking and breakthrough technologies-were determined and verified. Then, the impact mechanisms of the returns and initial proportion of breakthrough technologies on RIP evolution were dynamically and numerically simulated by Matlab. Results show that WoO is the best time for enterprises to implement RIP, and the three game results of RIP evolution of high-tech enterprises under WoO are only locking technology, only breakthrough technology, and both locking and breakthrough technologies, which occupy certain proportions in the market. Moreover, the returns of breakthrough technology play a decisive role in the evolution results of RIP, and the initial proportion of breakthrough technology affects the evolution speed of RIP. According to the research, the WoO-EGT model built in this study is feasible in dynamically analyzing the RIPs. The WoO-EGT model can help overcome the deficiencies of the static model of RIP and provide new decision-making ideas and methods for analyzing the RIPs of high-tech enterprises, thus contributing to the improvement of the success rates of radical innovation.