Tensor analogues of right 2-Engel elements in groups were introduced by D. P. Biddle and L.-C. Kappe. We investigate the properties of right 2-Engel tensor elements and introduce the concept of $2_{\otimes}$-Engel margin. With the help of these results we describe the structure of $2_{\otimes}$-Engel groups. In particular, we prove a tensor version of Levi's theorem for 2-Engel groups and determine tensor squares of two-generator $2_{\otimes}$-Engel $p$-groups.