To start off, I don't think Hitman is a stealth game more than it is a puzzle game. Every stage is its own open-ended puzzle that gives you multiple ways and tools to approach the situation any way you want.
It takes mechanics from older Hitmen, refines them and adds new ones. Gameplay has lots of details, such as peeking from keyholes, first person mode, concealing items, interacting with NPCs etc. Collecting guns from stages, and upgrading your weapons and items makes you feel you're constantly progressing and getting better. The stealth mechanics can feel a bit clunky today, but messing with disguises is still as fun as it was in 2006. The mechanics are also really easy to abuse and bug out, if you know how :P Still, getting a Silent Assassin rating, especially without any quicksaves is really satisfying.
Jesper Kyd's soundtrack is as amazing as it was in the previous Hitman games, I only wish Absolution and the new Hitman had his music :( It alone makes the game so much more immersive and gives every level life and energy.
Overall, Hitman: Blood Money still holds up really well today. Ignoring the tutorial mission, there isn't a single bad level in the game and they get constantly more complex along with your own progression. The amount of replay value it has makes it immortal for me.