First, what exactly is nihilism? I don't think we can pin down "exactly" what it is, so let's go with "roughly." Because you know I like it rough.
Nihilism was originally a kind of intellectual anarchism: all ideas should be held up to rational scrutiny, and what doesn't hold up should be discarded. The upshot of this tended to be atheism and moral skepticism, which was fairly shocking to many thinkers of the time. Mind you, this was the late 19th century, and many people still clung to the belief that ethics can only come from a divine lawgiver. (cf. Euthyphro: "Well then, what is dear to the gods is pious, what is not is impious.")
One of the best formulations of nihilism came from Nietzsche: "One interpretation of existence has been overthrown, but since it was held to be the interpretation, it seems as though there were no meaning in existence at all, as though everything were in vain." (Encyclopedia of Philosophy, vols. 5-6, p. 515)
The term "nihilist" has been watered down quite a bit in the past hundred years, partly because the word is used most often by religious people who want to use it as an epithet, like with "atheist" and "witch." And it's used quite often by dumb teenagers who have just started reading Nietzsche, not realizing that Nietzsche was actually opposed to nihilism.
Anyway. History lesson over. Down to brass tacks.
T-Rex is touching on a lot of different ideas here.
1) Values are baseless, and reasoning is impotent.
2) Nothing can be known or communicated.
3) Destruction is the natural response to this metaphysical collapse.
4) Life is absurd, and it is futile to do one's best in an absurd world.
Whether any of this counts as nihilism is not important; the term "nihilism" has always been a little vague, and these ideas seem a little more in line with existentialism (says the man who has studied the latter, but not the former...)
1) There is some truth to the statement that moral values are logically baseless. One of the things that has fascinated me in my study of ethics is that I am convinced ethics exist, but cannot pin down where or how, or how one might go about determining what they are. The best I have come up with is "it has something do with one's common society," which is not an answer that will satisfy anybody.
2) It doesn't happen to follow from what T-Rex says that nothing can be known or communicated. If he means nothing can be known infallibly, or communicated infallibly, then he is certainly right. But he is probably asking too much from the world if he expects infallibility, like expecting the milkman to also bring you bread, eggs, whiskey, and all of your other groceries, in addition to the milk. It is clear, though, that we do know things, and that we do communicate with each other.
3) ... this totally doesn't follow. Unless you want to talk about metaphysical destruction, in which case, this does not cover destruction of the log cabin.
4) Life may be absurd in the sense that its values are groundless and radically contingent, but it is up to each individual to decide on how to react to this. The key for the existentialists (and don't quote me on this) is that in a world where meanings are not inherent, we must attach our own meaning to things. Some people do their best at learning the natural sciences, while some people do their best at keeping up to date on the latest television shows.
Yeah, that's right. I said it. It is important to me to be up to date on American Idol and Family Guy. DON'T TRY TO FORCE YOUR VALUES ON ME!