Precisely. And in the sage advice they lay out a specific test to determine whether or not a thing fits into the second category and "seems magicky to me" isn't one of the criteria.
In fact, if you want to say that the frightened condition is always magical for the purposes of your role playing, there's nothing that specifically contradicts that. But unless the effect meets one of the criteria listed for inclusion in that second category of magic, by RAW, it's an effect that can't be dispelled, anti-magiced, or resisted by magical resistance.
As an example, a character targeted by a revenant's vengeful glare:
1) Can ignore the whole thing if they are immune to paralysis.
2) Has advantage on the saving throw if resistant to paralysis.
3) Can ignore the post-paralysis frightened condition of immune to frightened.
4) Gains no benefit from Halfling's Brave feature on the saving throw against paralysis, but does have advantage on subsequent saves against the frightened condition (or straight d20 if it can see the revenant)
5) Gains no benefit from magic resistance because there is nothing in the effect's description that would include it in the type of magic that can be dispelled, anti-magiced, or resisted by magic resistance.
That's the RAW.