It is well-known that EMVS-MIMO radar is an emerging technique that it allows for 2D-DOD and 2D-DOA estimation. Unfortunately, existing array geometries on the EMVS-MIMO radar can rarely reach a good compromise between the estimation accuracy and the computational burden. This paper is aimed at proposing an L-shaped sparse array topology for a bistatic EMVS-MIMO radar, whose inter-element distance is much larger than half-wavelength. A fast algorithm proposed herein to estimate the 2D-DOD and 2D-DOA. Firstly, the direction cosine estimates are obtained via the rotational invariance properties of the sparse subarrays, which are ambiguous yet exhibit high-resolution. Thereafter, the direction cosine estimates are achieved via the vector cross-product of the normalized Poynting vectors, which are unambiguous but have low-resolution. The unambiguous high-resolution direction cosine estimates are determined by combining the previous results, following which the 2D-DOD and 2D-DOA can be easily recovered. It is shown that the proposed framework can obtain a better accuracy of estimation than the other existing methods. Moreover, it is more flexible than the current sparse array methodologies. Finally, the theoretical derivations have been validated by simulation results.