The latest developments in terms of self-driving technologies have increased the demand for high quality data transmission in vehicular networks. However, frequent handovers among the Road Side Units (RSUs) cause degradation of data transmission performance, especially in the context of high-speed mobility. In order to address this problem, a novel game-enhanced compensation handover scheme (GCH-MV) for multipath TCP in 6G software defined vehicular networks is proposed. An innovative system architecture which integrates 6G communication solutions, SDN and multipath techniques is presented. GCH-MV redesigns the fluid model of Multipath TCP (MPTCP) to compensate for the declining throughput by using multiple paths. GCH-MV transfers traffic quickly between different paths, adapting the transmission to path quality and maintain high throughput. In addition, an innovative game-based optimal candidate RSU selection algorithm, employed by GCH-MV during the handover process, is also introduced. GCH-MV uses these solutions to achieve its goal to mitigate the negative impact of handover as much as possible and make the handover process smooth and transparent. Experimental results show how GCH-MV outperforms the existing solutions in terms of several quality of service (QoS) metrics, addressing efficiently the data transfer quality problem during handover in highly mobile vehicular networks.