https://en.wikipedia.org/wiki/The_Darkness_(video_game)
Release date: June 25, 2007
The Darkness was pretty much Starbreeze's successor to Riddick, in that it combined a more-or-less linear shooter campaign with some NPC interactions between levels. I remember my mind being kinda blown by how you could watch whole TV shows in-game.
It was one of those games that had a "next-gen" feel at the time, without being an exceptional game. I associate with stuff like Lost Planet and the original Prey in my mind. They were cool proofs-of-concept for the 360 while devs were still learning to adapt to the demands of the hardware. Bioshock would arrive that August, after which it felt like the PS2 era was left behind for good.
Gameplay: https://www.youtube.com/watch?v=VaY7wU_r__o
It also looks considerably worse than I remember. It was released right at the height of the "shiny walls and a fuckload of bloom" era.
It was also the game featured on the first-ever episode of Zero Punctuation: https://www.youtube.com/watch?v=eWS9_nrKOPA