Now, I would like to tackle the "time" component.
As stated before, its a simplification.
Our game could have levels, bosses, quests or other means of progressing.
We dont know, but generally they will be sequenced in some way,
 therefor time suffices to what is some arbitrary game state we find significant.
For a concrete game, we *could* be better of specifying whatever is appropriate.

What we shouldn't do however, is whatever the fuck Tom Smith thinks he is doing
 in Anatomy of Game Design page 263:

    > Giving players more agency gives players the ability
    > to adjust this curve on their own, which is a powerful way to make
    > sure the difficulty curve adjusts to each player’s needs.

    = Grant Theft Auto 3 Difficulty curve =
         
      │      ooooooo ^^^^ oooo
      │oooooo       ^oooo^    ooooooo
      │            ^            ....
      │^^^ .... ^^^   ....^^ ...  ^ .
      │....    .......    ...
      │
      └───────────────────────────────

    > This form of difficulty tracking is mostly intended for video games where
    > there is a long sequence of single-player content for the player to consume
    > in a linear fashion. GTA3 breaks this rule by not following a linear
    > sequence.

He is perfectly correct on the first part.

However, he should have never drawn whatever eye cancer that is.
He took time literally, making his data into a sausage-blob.

Instead, one is meant to break it down into missions.
Then maybe sort it by average playtime of entering
 and -with rigorous cross checking of retention data-
 identify pacing issues.

---

What about multiplayer games?

Team Fortress 2 would have a curve.
What it most certainly wouldn't have is this thing:
    ▲ skill       
    │   ....      
    │   :         
    │...: experience
    ┼───────▶
Which is proof that r*dditors are incapable of reading graphs,
 and would mean that things click suddenly and you ascend to godhood.
Anyways, the curve is fine:
 yeah, I got backstabbed for 18th time,
 but I keep oneshotting the enemy heavy so I'm still having fun.
That is to say, large teams and short kill times makes it possible
 to focus on frags within my skill level, making the difficulty feel flat(ish).

Track Mania speed running would have an exponential curve,
 but I only need to beat my own record to feel accomplished.

Counter Strike would have a curve, but the match making always places me
 with players of similar skill level.
Wait, wait, wait? Similar skill level?
Does that mean we can measure skill?