Enemy fire here seems to be those red phaser-style beams; the green streaks and strobes might represent another kind of enemy fire, but also perhaps the environment: a weird nebula, a planet's upper atmosphere, a Romulan time tunnel? This environment might affect the way the smoke swirls and the gasoline explosions billow.
But probably the battle visuals will be no more "realistic" here than elsewhere in scifi. It's not as if anybody ever has had any sort of interest in such a thing, not in Trek or Wars, but also not in Babylon 5 or nu-BSG, which considered "gritty realism" a selling point.
I do wonder what the effects would have looked like if some of the shots exchanged in ST:TMP had pierced through shields to the hulls...