Spotify does not transfer the audio stream itself, only the control channel. Your audio gets pulled directly from Spotify on the tablet.
TO be honest, I don't know of easy solution for that. Two pieces of software are needed, one for the PC (emulating a sound card where you can route audio output), one for the tablet (to play the stream). Couple of years ago I bought a "network audio player", which provided the PC software, and comprised of a box with Ethernet and audio out connection.