If this question is asking what minimum equipment have I found it necessary to have available in order to run an enjoyable and successful game, then the answer is short and simple.
- At least one other imaginative player.
I've run successful games for a single player. I've run successful games purely freeform, ad libbed, at conventions for paying players who wanted to come back and play again. I will admit that the first games (with a single player) did feature a lot of props, miniatures and the whole RPG experience, but I really think I could play a successful and fun game with no props, no system, no preconceived story and only a single player.
If the question is asking what I usually carry in my roleplaying kit as my typical gaming gear, then there's a bit more to add.
- A couple of imaginative players
- Some pencils and notepads
Then, slightly less essential...
- Character details (whether on character sheets, index cards, or whatever)
- Some food and drink, if we know we're going to be at this for a while
- (At least one PDF or hardcopy of the game being run, and any randomisers associated with the game)
- (Some figures and wooden blocks to replicate buildings/corridors/dungeon-walls/obstacles, if we're playing the kind of tactical gamer that might need it)
I usually go even further than this, but the listing provided is what I'd usually bring to a game.