paralipsis: I think there are a couple of things that contributed to that.
Firstly, if you compare Turok 2 enemies to those in Doom, their movement patterns are less linear. On its own that wouldn't be too big of an issue, but when you pair it up with the choppy frame rates the original release had, it could feel like you are missing because of the interface more than your own skill level.
This new version essentially solves the frame rate issue, but it is still a game where enemies bounce around your field of view more than those in Doom (or pretty much any other game with sprite-based enemies that spring to mind). For that reason, I do miss shots more than when I play some other games, but it doesn't feel like laggy controls to me, but rather a greater demand for precision due to enemy movement patterns.
Another thing I noticed is that the movement controls are even laggier than the aiming controls. Often I don't manage to dodge enemy shots because Turok will move half a second after pressing the strafe button. After years of responsive shooters, it's very difficult to digest.
On a side note: I tried the N64 version. It's even worse than the PC version, in high resolution mode in particular it takes almost a full second before Turok starts moving in the direction you want him to. It makes me wonder how low console standards must have been, if this was considered a great game in its time.
For a quick comparison, Turok Rage Wars isn't nearly as bad, so at least part of the issue must have been a design decision - maybe they wanted Turok to move more slowly so the game would feel less like a Doom clone.