If you have existing chimney with a good draft, you can remove the Direct Vent and run it directly into your chimney. You will need a Baro Damper if not using your Direct Vent to adjust the draft correctly on the stove. You should have a draft gauge that you can adjust it correctly.
Running the DV up and into chimney is also ok. as long you don't have any other appliances sharing the same chimney, the DV could pressurize it and back feed into the other holes and come out somewhere else. Just be careful!
My keystoker is running a pipe up and outside, I had an existing hole in the wall near the ceiling and it runs up and over and outside.