Finally, for the audience's sake, we see what the landing party cannot: the ship vanishing from orbit--proving that Flint's power was not trickery or illusion.
Kirk looking in through the bridge viewscreen, as though it were a window, is a similar "shorthand." I don't think the audience is meant to take it literally. What matters is that whatever Kirk was shown was convincing evidence of Flint's power.
One of the limitations of the TOS-R effects is that they all had to fit into the same space as the older VFX they were replacing. Assuming a complete "remake," how might Flynn's powers have been depicted—in a way compelling to both Kirk and the audience?