I think that's a big part of it, viewed from one angle. Another angle might be related to immersion. Some might say that if the DM wants a PC to be intimidated, he should telegraph the danger represented by the intimidating individual, so the player appropriately fears for his character (with whom he identifies enough that he reacts as an intimidated character would).
Intimidation is more than just being scary, it's being scary, but also not implacable, with a clear course of action that will remove the implied threat. It means being credible on both sides of that equation, that you /are/ dangerous, that you /will/ do something horrible, but that you'll refrain if the victim knuckles under. Just being scary is just being scary, like a dragon fear aura, for instance - it's /really/ scary, but characters affected by it don't start doing what the dragon tells them.
The angle I like to look at it from is more a matter of resolution. An NPC tries to intimidate a PC. How do you resolve that? Does the DM just tell the PC how he reacts? (resolution by DM fiat) Does he just describe that the NPC is intimidating and let the player declare his next action? (player fiat) Do the DM & player 'RP' the intimidation? (Player as resolution system) Or, do they use a sub-system provided by the game? (Like a check or opposed check) In 5e, the official resolution system is the player declaring an action and the DM narrating the result, with checks optional - but an NPC intimidating a PC isn't a player action, is it? ....