No you don't, you have the definitive edition which isn't just Sleeping Dogs with the DLC added, it's another version. "The Definitive Edition of the critically acclaimed, award winning open-world action adventure, reworked, rebuilt and re-mastered for the new generation. With all previously available DLC included and a wealth of tech and visual improvements, Hong Kong has never felt so alive."

https://store.steampowered.com/app/307690/Sleeping_Dogs_Definitive_Edition/