Gasp out is a phrasal communicational verb that means, roughly 'say, with sound effect of gasping'. So it's transitive, but that's because of the construction frame
human sound/visual effect +
direct/indirect dialog chunk] (+ out)
- (not necessarily in this order] (final particle optional; out is only one of several)
becomes a manner of speaking verb (or, quite often, phrasal verb):
manner-of-speaking verb +
direct/indirect dialog chunk]
followed, in the case of phrasal verbs like gasp out, by a particle ("intransitive preposition")
or by transitivizing prepositions to allow objects, like the ones in
Yell to George about the new quota.
There are lots of constructions that use these verbs this way, e.g,
- "Go to hell!", he sneered/snarled/barked/gasped/whispered/ ...
In a construction like that, one needs no out, though it's usually OK:
- "Go to hell!", he sneered/snarled/barked/gasped/??whispered/ out
I conjecture that whisper out is problematic because whisper is already a speech verb. What I'm calling "Speechification out" comes from the experience of emitting language, through various means, for various purposes, with various effects. It's a semantic addition to a human voice or facial or body communication effect that converts it -- if it takes [and it often doesn't, he winked] -- into a metaphorical speech verb.
Turns out how people talk is something people talk about a lot, and consequently it has lots of specializations in its language, like the English human motion verbs or verbs of cutting. Most are metaphors, and most are seriously context-dependent.