What is the native Mac Chess app's rating? Is there a good alternative? I can't find anywhere what the rating of the Mac's native Chess app is at each level. 

Is there a Chess app for Mac that shows the strength bar during the game?
The Mac Chess app engine is the Sjeng engine.

On the old Sjeng website (because Apple Chess is using the old Sjeng) is says:


  For standard chess, Sjeng's rating is probably about 2450 ELO


And I'm assuming that is at its best.

As for looking at each level, there isn't much of a way to know because, beyond the 3 moves ahead area, it starts counting in seconds, and in that realm it depends on the power of the computer. The more powerful the computer, the better it plays because it can look more moves ahead in that time.

TLDR - An estimated 2450 at it's best. It's not a very powerful engine, but it can still whoop most players on it's hardest difficulty.