It's not like we see transporters capable of beaming in an arc like fashion. They have to be in range of the coordinates, and that probably means "line of sight" in the sense of it being a mostly straight pathway. I obviously didn't mean "clearly visible" as we have so many examples of people beaming inside buildings and beneath layers of rock.
I actually think it makes much
more sense that Flint would've had a disabling power beam on the Enterprise, essentially "suspending" it in mechanical, electrical, and life sign form, then rapidly produce a miniature copy (scanned from the original) appearing on the table. I know the episode wasn't written that way, as we see the Enterprise wink out of orbit and Kirk's face show up on the view screen, but it was probably done because of the ease of SFX (not unlike the transporters versus a shuttle craft). If Flint could really do what he appeared to have done, then... the ryetalyn could have been materialized for Kirk in mere minutes and they'd have been on their way. Of course, that wouldn't make for much of a story.