For the benefit of those of you wanting to know more about either Sleeping Dogs or the Definitive Edition, take a load off and have a seat.
One aspect of the original release of Sleeping Dogs that a lot of people liked was the story, so let's start there: You are Wei Shen, an undercover cop who is tasked with infiltrating the Hong Kong Triads. As Wei rises through the Triad ranks, questions arise about his loyalty to both criminals and cops and he must strike a fine balance between underworld enforcer and undercover officer.
The open world of Hong Kong will see you free running, vaulting and racing through a city of dingy back alleys and glamorous high streets while doing whatever you want - completing story chapters or side missions, finding collectibles, winning vehicle races or simply getting down and dirty in fight clubs…
Which brings me to the combat aspect. Sleeping Dogs focuses heavily on stylised melee combat, particularly martial arts. This involves a system based on counter-moves and bone crunching combo attacks, as well as a heavy sprinkling of environmental kills. You will of course be able to find and use a variety of guns throughout the world, but they aren't everywhere. You'd therefore better work on throwing those punches rather than bulking up that trigger finger!
That's the Sleeping Dogs base game… now for awesome stuff the Definitive Edition adds… It integrates over 20 DLC packs, which includes outfits with special perks or combat moves, new cars (one of which is mounted with twin miniguns and an EMP) and of course story extending packs that add at least three hours of story gameplay.
Source: The Developer Website.