So the player says "I grab a rock and crush it with my bare hands while looking at him menacingly".
They are trying to intimidate, but they are using their muscles to do it.
I suppose you'd ask for a Strength check. Would it be Strength(Intimidate) or Strength(Athletics), or let the PC pick?
Well, here’s the thing. I assess whether a check is required and if so with what ability and at what DC based on both the approach (in this case grabbing a rock and crushing it with their bare hands while looking at the NPC menacingly) and the goal (in this case, presumably getting the NPC to do something they want).
So first I’d ask myself, does this approach have a reasonable chance of succeeding in accomplishing the goal? This will depend on the specifics of what the player wants to get the NPC to do, as well as the personality and character traits of the the NPC in question, but for the sake of this example let’s assume the answer is yes. Likewise for if the approach has a reasonable chance of failing to accomplish the goal.
Once I’ve established that success and failure are both possibilities, I would ask myself if there’s a cost for the attempt or a consequence for failure. This will again depend on the personality of the NPC, as well as the circumstances under which the action is taking place. If there is no cost or consequence, I’ll just default to the action succeeding and narrate the results. Again, for the sake of this example, let’s assume there is a cost or consequence. Maybe this NPC doesn’t respond well to threats and is therefore liable to become hostile on a failure. Ok, stakes established.
If I’ve gotten this far, it’s time to decide the appropriate ability to check and the difficulty. So I go back to the goal and the approach and ask myself what ability would this approach hinge upon to be successful at achieving this goal. Does being stronger make the crushing of a rock while starring at someone more likely to get them to do what you want? Personally, I don’t think so. If the NPC is going to be cowed into doing what you ask by seeing you crush a rock, they’re going to be cowed by it no matter how big your muscles are. What this action accomplishing this goal really depends most on, if you ask me, is how convincingly you can sell the implicit “this will be your head if you don’t comply,” and that’s all in the stare. That’s a Charisma check.
Finally, I’ll decide if it’s easy, medium, or hard. Since we’ve established that this character doesn’t respond well to threats, I’m thinking hard. So I ask the player to “Make a DC 20 Charisma check. On a fail, he’ll become hostile.”
Now, the player is free to decide if any of their Proficiencies are appropriate to add to the check. Intimidation and Athletics both seem like obvious choices to me. A less obvious but still entirely appropriate proficiency to add might be mason’s tools, reasoning that knowledge of stoneworking would allow the character to know the best way to apply pressure to make the rock break more easily. A dwarf character might even use the same reasoning to apply double their proficiency bonus for Stonecunning.