Yes, you absolutely walk between the two parks (through the esplanade) to get to DTD. The reason google has you walking around DL is because google only follows actual roads/streets when giving directions, and the walkway between the parks in not a road. (If that makes sense.)
The walk is maybe 4 minutes at most, and you will need to go through security/bag check before entering the esplanade, but once you get through security, it's clear sailing to DTD.