The flying speed of autonomous quadrotors has increased significantly over the past 5 years, particularly in the field of autonomous drone racing. However, most research primarily focuses on the aggressive flight of a single quadrotor, simplifying the racing gate traversal problem to a waypoint passing problem that neglects the orientations of the racing gates. In this paper, we propose a systematic method called Pairwise Model Predictive Control (PMPC) that can guide two quadrotors online to navigate racing gates with minimal time and without collisions. The flight task is initially simplified as a point-mass model waypoint passing problem to provide analytical time optimal reference through an efficient two-step velocity search method. Subsequently, we utilize the spatial configuration of the racing track to compute the optimal heading at each gate, maximizing the visibility of subsequent gates for the quadrotors. To address varying gate orientations, we introduce a novel Magnetic Induction Line-based spatial curve to guide the quadrotors through racing gates of different orientations. Furthermore, we formulate a nonlinear optimization problem that uses the point-mass trajectory as initial values and references to enhance solving efficiency, enabling the method to run onboard at a frequency of 200 Hz. The feasibility of the proposed method is validated through both simulation and real-world experiments. In real-world tests, the two quadrotors achieved a top speed of 6.1 m/s on a 7-waypoint racing track within a compact flying arena of 5 m * 4 m * 2 m.