LCD screens do not refresh like CRTs. For example, turn a CRT down to 60Hz, now look to the side, you see a "flickering" because your peripheral vision is inherantly better at seeing motion. Now turn it up to 85Hz, look away, and notice the flickering is much less.
Some of us have better eyes, or
onder: better trained eyes. At first glance I can determine immediately if a monitor is at 60, 85, or 100Hz. The difference is quite pronounced, and has a large impact on eye strain.
LCDs do not suffer from this condition. A Pixel is made of 3 parts that are either ON, or OFF. There is no sweeping electron gun. This results in less eye strain.
As for the 60Hz and gaming. Most games support Vsynch. Vsynch is a way to limit the framerate to match your refresh. Why is this needed? Many games experience TEARING if you look around quickly or scroll quickly. This is because each frame is drawn as fast as possible, and sometimes you get caught mid-refresh with a new frame, and so a tear occurs. If you limit the framerate, then the overall image is much smoother.
Unfortunately not all computers are capable of 60fps+ operation in a game ALL the time. So in cases where Framerate drops below 60fps, the framelimiter kicks it down to 30fps - and this can cause noticeable lag for a second as everything adjusts - then when 60fps or more is possible, the game pops back up to 60. The end result can be a LOT of stuttering on games you are borderline 60fps (or whatever refresh you use).
Now a method called triple buffering exists by which alleviates this problem, but it has it's own caveats (limited support, sometimes buggy).
As for eye strain, well I do experience it on my 1920x1200 resolution LG truelife glossy XPS Gen2 display. However, what do you expect with text so small? Truly it took some getting used to at first. For one, sit closer. Second, make sure you have a decent amount of ambient light. Using my laptop in a dark room really hurts. The screen is too bright.
Some other ideas have already been mentioned. Truth be told I love the screen. I can use it outside or in the car, wheras my Matte screens all get faded beyond recognition. It's awesome for movies, coding (can fit so much code on the screen at once), and for gaming.
I find most games run fine at 1920x1200 or 1680x1050. Simcity 4, KOTOR2, WC3, HL2, BF2, Sims 2, Black and white2, DDO, CoH, WoW, Kohan2, etc. etc. Only a very few games have needed extensive hacking to get working.
So take it for what it's worth. The high-res screen isn't for everyone. But it's worth a shot if you're like me, and need the versatility! Good luck reducing the eye strain