That's just the way MIDI works. You need something to read the MIDI data, interpret it, and then play the appropriate sound. When you send the MIDI out to your DD-65, the DD-65 is changing the MIDI data into audio. When you send the MIDI data from the DD-65 into your computer, you need a virtual instrument to interpret the MIDI data and produce sound. If you don't have a DD-65 virtual instrument, you won't get the DD-65 sound with MIDI.
As you mentioned, you can record the audio output of the DD-65 to capture its sound.
There isn't a virtual instrument that has the drum sound you want?