Is it supposed to run this fast? Sometimes the sounds cut off right in the middle so I guess the speed isn't supposed to be this high...

After some experimenting the fast speed is intentional, even after limiting the FPS to be safe it still is REALLY fast.

But how does the speed compare to the original game?

The original, at least on the N64, is VERY sluggish thanks to the hardware and the original PC port was faster, but still had the slowness of the N64 version's thanks to being an almost straight port. This one feels a lot more Quake like in its pacing which after playing for a bit, I got used to. Turok has been labeled as Jungle Quake and now it feels like it really lives up to that title.

So it's just a matter of sprint speed? The game isn't running too fast, is it? (that would not be good)

Ok, based on some time playing around with it, on normal it is a bit faster than the original but in a playable way since it is running at 60 FPS and what not with no framerate dips. When you go to hard difficulty, the game makes the enemies run and attack WAY too fast. I am not sure if that is intentional or a bug.