I love atmosphere, immersion, challenges and interactivity in games.
Dark Souls 3 is great example of this, with great atmosphere and somewhat immersive world, while being a great challenge (I soloed on final boss with BKUGS, full BK set and fully loaded pyromancies - had to repeat more than 50 times). It was a bit lacking in interactivity, but breakables and occasional lever/switch did the job for me.
Morrowind is really great game combining all of the above factors - it is extremely immersive, has just perfect atmosphere of being stranded in weird, almost alien world. Interactivity was done mostly through scripts, but it was varied and entertaining. Also, early levels provide a good challenge for some builds.
As far as interactivity goes, I loved being able to pick up and throw objects in Half-Life 2, also gravity gun and (really simple) physics puzzles. Interactive panels, GUIs on weapons and PDA just rocked in Doom 3.
Damn, I could go on and on with games like Blood (gothic or world war 1 era atmosphere, challenge - Deathmask style, interactivity - kicking zombie heads, playing piano, one-liners when using objcts) or S.T.A.L.K.E.R series (being stuck in the zone, A-Life, creepy labs).
I also like simple, competitive games, like World of Tanks. Speaking of which: