The major problem (which is addressed in the article, by the way) is that once you've set a course you can't really change it much at all. Newtonian mechanics really limits your options here. Warships and space battles would be completely preprogrammed: detect enemy ship; set course for enemy ship; accelerate to maximum velocity; attempt to kill enemy ship with automated systems and not die as you shoot past.
This isn't really an "engagement" as we think of it now, it's more of just a fire-and-pray scenario.
Once you fire a rifle, everything is also Newtonian and deterministic. You still have to move into position, decide which target to fire at, with what ammo etc
What you describe is quite close to an actual weapon used in WW2, the SG 500:
It doesn't follow in every case, but here the calculations are things like missile ranges, acceleration values, maximum speed, etc. These all seem to be rather simple Newtonian calculations.
Basically the problem dilutes down to: plot an intercept course, fire weapons, rinse, repeat.
This isn't really an "engagement" as we think of it now, it's more of just a fire-and-pray scenario.