I have never played Hitman, but I went to watch the movie anyway. The Hitman in question is a nattily dressed bald guy with a barcode tattooed on the back of his head. How that makes him inconspicuous in a crowd, I wouldn't know.
His backstory gives him a reason for being as emotional as a hypothermic doorstop. He, and many others like him, have been raised from childhood as smart, efficient killing machines by the nameless Organization. Its clientèle are none less than political heads of state who order clandestine hits for reasons Joe Voter will never understand. The Hitmen are that good, and that expensive. No doubt the Organization itself has an agenda to run in its own interest.
In this movie, Number 47 takes the job of assassinating the Russian president, but realizes very quickly that his client has set him up. His client's agenda is so sensitive that even the Hitman himself has to be eliminated as a potential witness. 47 then has to survive hits from his own colleagues and the Russian secret police, and dodge a persistent Interpol officer hot on the trail of a phantom killer. Meanwhile, out of the goodness of his heart, he protects another witness: a woman who keeps taking her clothes off for him only to be rejected and rebuffed every time. No distractions on the job, or while trying to stay alive, 47 is such a pragmatist.
In whatever situation 47 is in, he firmly remains in control. On the job, his preparations are extensive, every detail thought through, ensuring a clean hit and getaway. His fighting skills get him out of unexpected situations, and at no time do we feel 47 is in any danger. For him, everything that happens is part of his plan, and he does have a lot of foresight.
Perhaps that's why we can't really get into the story much. Our sympathies are more for the bad guys as we wonder what 47 has in store for them, rather than for 47 himself. With the protagonist this strong and invincible, we just coast through the narrative. Though we may revel in the carnage of gunplay and thrill to the swordfighting sequence, the experience is like playing on God-mode. You get to finish the story, but there's little sense of accomplishment at the end.