My game crashes repeatadly and the only suspect I have is my GPU. It is a Nvidia GTX 770, which is above the minimum requirements but it crashes on some maps in specific locations. For example: Ambrose Island at the destroyed castle. I have set the quality to lowest and limited FPS to 30 fps, but it still happens.

Seriously??? It ran like crap on my SLI 980's at 4K, so I doubt a GTX 770 is really going to run it.
Granted, I did check the minimum requirements and you are correct - they did state that the minimum was a GTX 660, but I wouldn't trust this since the GTX 660 was released 4 years before the first Hitman game (in the Trilogy) was released; and again, your GTX 770 was released 3 years before the first game in the trilogy. The game has gotten small graphical updates since Hitman 2016, but you are now essentially playing the game with a 10 year old graphics card.

If I'm not mistaken as well, that card only has 2Gb VRAM... You'd be lucky to play any game in the last 10 years on that card I suspect... Even GTA IV could sometimes hit the 2Gb VRAM limit if you were playing on a 1440p monitor with everything on very high and that game is 15 years old.

Even the GTX 690 was faster and had double the VRAM of the GTX 770. I know because I bought a GTX 690 in December 2012... that was a glorious piece of architecture.