We quantize the two-dimensional projectable Horava-Lifshitz gravity with a bi-local as well as spacelike wormhole interaction. The resulting quantum Hamiltonian coincides with the one obtained through summing over all genus in the string field theory for two-dimensional causal dynamical triangulations. This implies that our wormhole interaction can be interpreted as a splitting or joining interaction of one-dimensional strings. (C) 2021 The Author(s). Published by Elsevier B.V.