I haven't looked closely at the full construction, but it's fairly similar to an earlier paper by Cash et al. (https://eprint.iacr.org/2014/853) which is surprisingly practical - their system can do keyword searches on the entire English Wikipedia in just a couple seconds.

In terms of security, things are a bit more complicated. The last ~year has seen a couple papers (https://eprint.iacr.org/2016/718 and https://eprint.iacr.org/2016/172) that demonstrate damaging and practical attacks against most SSE constructions. It's really not clear how secure any SSE scheme is in practice, or whether there is a sensible model in which SSE can be both secure and efficient enough for practical use.