Alright, I'm going to try and break this down... there are actually 3 entirely seperate things people are talking about here: simulation frame rate, rendering frame rate, and monitor refresh rate.
'Hurtz' or 'hz' are a universal term that just means "X whatevers per second", so having 60FPS means your card is rendering at 60hz.
Now, in the post Carmack says nothing about monitor refresh rate, so that really isn't anything to worry about. Your monitor will still refresh at whatever you want it to refresh at, within it's capabilities. The other two things, the simulation rate and the rendering rate are both going to be locked at 60hz/FPS.
Let me try an analogy. Let's say you are in a room, and next door there is a chess match. The frequency at which the chess pieces are moved is the simulation or game rate. Now if you have someone taking a polaroid snapshot at a certain rate, that is the rendering rate, what everyone knows as FPS. If someone else is taking those photographs and bringing them to you, that is like your monitors refresh rate.
This isn't a perfect analogy, but it's good enough to illustrate the point: if the chess pieces only move once per minute, no matter how often someone takes a picture of it, it will always look the same.
60hz is a big leap for the games simulation rate though, if i recall correctly quake 3 ran at around 20 to 25 by default, but you would see inbetween stuff due to a trick called interpolation. The statement in the article seems to imply that doom 3 won't be doing any interpolation, which I think is the most interesting aspect of the comment.