@Phaser Two wins it. It is the Caretaker. You have the game.
Clue 1: I don't judge your lifestyle.
Clue 2: I can be very industrial, too.
Clue 3: I seem quite jolly, too.
Clue 4: I'm impressed with the Captain, too.
Clue 5: I'm probably too complicated for you to understand.
Clue 6: You only see me as a representative of my race, but are you really seeing the real me?
Clue 7: I have mastery over life and death and life again.
1. He was willing to create any fantasy: sexy women, rapist, murderers, enemy soldiers, old rivals, anything.
CARETAKER: But none of this is permanent. Here you have to only imagine your fondest wishes, either old ones you wish to relive or new ones, anything at all. Battle, fear, love, triumph. Anything that pleases you can be made to happen.
2. He could whip out anything you want: pistols, planes, tigers, women, knights on horses, dresses, anything.
MCCOY: They've got a factory complex down there you wouldn't believe. They can build or do anything immediately.
3. He greets Kirk with a huge smile and makes a fun offer to him:
CARETAKER: If you would use the proper caution, this amusement planet of ours could be an ideal place for your people to enjoy themselves, if you wish.
4. He complimented Kirk on his understanding the purpose of the planet.
KIRK: Yes, play, Mister Sulu. The more complex the mind, the greater the need for the simplicity of play.
CARETAKER: Exactly, Captain. How very perceptive of you.
5. Kirk asks who they are:
KIRK: You say your people built all this. Who are you? What planet are you from?
CARETAKER: My impression is that your race is not yet ready to understand us, Captain.
6. The Caretaker is from a highly advanced race, so, we may not be seeing a true appearance. The Caretaker says "we", so, their may be more of them on the planet:
CARETAKER: We regret that some of you've been made uncomfortable.
7. They create seemingly living beings which you can kill. Also, living beings who visit the planet can be killed, only to be brought back to life again such as McCoy.
KIRK: But that still doesn't explain the death of my ship's surgeon.
MCCOY: Possibly because no one has died, Jim. (Strolls in with a lovely girl on each arm) I was taken below the surface for some rather remarkable repairs. It's amazing.
Sub-clue: It's amazing that so many answers can fit the clues
with imagination and thought.