This is an unfair comparison because you could include the gory details in the first example, too. Flourishes like that don't have anything to do with mechanical transparency. A lot of games show the difficulty right on the character sheet, including classic D&D with saving throws. I don't think having those numbers available to the player inherently negates immersion.It’s really about how cleverly you operate the rules. I would never tell players they need a 9 to hit. Or that they need a 12 to disarm the trap. Or they need 12 damage to kill the monster. That's not immersive. They could eventually deduce those things after repeated attempts (if they really want to) but they aren’t told those things outright.
The goal isn’t to reproduce a video game but rather replicate the tension you might experience if you were to actually encounter these things.
But to be clear, all this isn't what I'm talking about when I mean challenge. I mean in-game challenges to the characters like the monsters themselves, traps, puzzles, mysteries that require player's head to help solve. Things like hiding the system ("roll a 12 to hit," "you take 7 hit points damage") are more to do with immersion than challenge.
Look at these two scenarios, though, for how mystery and tension can be added to standard monsters:
Scenario 1:
Player: I attack the orc
DM: Ok, roll, you need a 12.
Player: I roll a 15.
DM: Ok, you hit, roll your damage. You need a 4.
Player: I roll a 6.
DM: Ok, it's dead.
Scenario 2:
Player: I attack the orc
DM: Ok, what weapon are you using? Roll to attack.
Player: I'm using my magic broadword. I roll a 15.
DM: You plunge the sword into its shoulder. Roll your damage.
Player: I roll a 6
DM: Your sword cleaves through its shoulder and down through its chest and the orc falls in a bloody heap, dead.
The first is mechanical and uninteresting. The second leaves open the mystery of how dangerous the orc was, and how difficult it would be to kill even though everyone knows generally how difficult orcs are. If you amped or changed the stats for the particular orc, you leave open room for surprise and strangeness in the encounter -- "hey, this orc isn't acting like a typical orc!"
Of course, I don't think immersion is particularly important in enjoying RPGs, but many folks consider it paramount. To achieve I think you need Free Kreigspiel levels of system opaqueness and I don't think most players want that.