Another issue is that also as the temperature increases, the metal components also slightly increase in size. How much this effects the ability to function I'm not sure, as the increase is still small while the temperature increase is small.
My understanding is that the temperature warning doesn't so much warn you that things are too hot, but rather that the coolant is not acting sufficiently at taking the heat away from the engine. If the temperature reaches 100 degrees centigrade, then there is actually minimal water in the system, but rather steam. This steam is substantially less effective at heat transfer than liquid water. You therefore get a positive feedback cycle, and this easily runs away on you and the engine gets to extreme temperatures, and this is when the damage is caused.
Your question more asks what does damage the engine. I suspect it is a combination of the reduction in viscosity resulting in less lubrication, and also the slight swelling - which at 200 degrees is more of a noticeable increase. Furthermore at that temperature there could be some alterations of the chemical properties of your coolants and fuels, which cause differing effects than what the engine was designed for. Also at high temperatures your rubber/plastic seals can begin to deform and denature, reducing the effectiveness of them.