Reading it more and talking to others... it's definitely the second case. Comes down to this specific line: Make a secondary attack, which has the fear keyword. Basically, it becomes a fear attack only (having a burst 3 range is pretty much a dead give away). It's a straight Con attack.
If it was the 1st case and you basically get Invigorating, Martial, Weapon & Fear... damn, that'll definitely be broken. 1st off, Hammer Rythm will be insane. 2nd, you're almost (99%) guaranteed to hit getting THP. 3rd, there's a possibility that it will stack if you hit multiple targets with the secondary attack.
It makes a bit more sense with the character I have it on - he's also got Draconic Arrogance, so he damages on a hit as well.3: RAW, Hammer Rhythm does apply its damage to the enemies that you miss with the fear aspect of the power. And yes, that's wtf. But that's more because the wording of Hammer Rhythm doesn't care if you'd normally deal damage on a hit.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.