Some of the rationality may to significant extent be a subset of standard, but it has important omissions - in the areas of game theory for instance - and much more importantly significant miss-application such as taking the theoretically ideal approaches given infinite computing power as the ideal, and seeing as the best try the approximations to them which are grossly sub-optimal on the limited hardware where different algorithms have to be employed instead. One has to also understand that in practice computations have cost, and any form of fuzzy reasoning (anything other than very well verified mathematical proof) accumulates errors with each step, regardless of whenever it is 'biased' or not.
Choosing such a source for self education is definitely not common. As is the undue focus on what is 'wrong' about thinking (e.g. lists of biases) rather than on more effective alternatives to biases; if you remove the biases that won't in itself give you extra powers of rational thinking; your reasoning will be as sloppy as before and you'll simply be wrong in an unusual way (for instance you'll end up believing in unfalsifiable unjustified propositions other than God; it seems to me that this has occurred in practice)
edit: Note: he asked a question, I'm answering why it is seen as fringe, it may sound like unfair critique but I am just explaining what it looks like from outside. The world is not fair; if you use dense non-standard jargon, that raises the costs, and lowers the expected utility of reading what you wrote (because most people using non-standard jargon don't really have anything new to say). Processing has non zero utility cost, that must be understood, if the mainstream rationalists don't instantly see you as worth reading, they won't read you, that's only rational on their part. You must allow for other agents to act rationally. It is not always rational to even read an argument.
Actually, given that one could only read some small fraction of rationality related material, it is irrational to read anything but known best material, where you have some assurance that the authors have good understanding of the topic, including those parts that are not exciting, or seem too elementary, or go counter to the optimism - the sort of assurance you get when the authors of the material have advanced degrees.
edit: formatting, somewhat expanded.
I don't have enough knowledge to agree/disagree with points before your "edit: Note."
I do agree with what you said after that. And applying your own advice, please add some paragraph breaks to your post. If nothing else, add a break between "extra powers of rational thinking" and "he asked a question." It should make your post much easier to read and, as a consequence, more people are likely to read it.
I've spent so much time in the cogsci literature that I know the LW approach to rationality is basically the mainstream cogsci approach to rationality (plus some extra stuff about, e.g., language), but... do other people not know this? Do people one step removed from LessWrong — say, in the 'atheist' and 'skeptic' communities — not know this? If this is causing credibility problems in our broader community, it'd be relatively easy to show people that Less Wrong is not, in fact, a "fringe" approach to rationality.
For example, here's Oaksford & Chater in the second chapter to the (excellent) new Oxford Handbook of Thinking and Reasoning, the one on normative systems of rationality:
Is it meaningful to attempt to develop a general theory of rationality at all? We might tentatively suggest that it is a prima facie sign of irrationality to believe in alien abduction, or to will a sports team to win in order to increase their chance of victory. But these views or actions might be entirely rational, given suitably nonstandard background beliefs about other alien activity and the general efficacy of psychic powers. Irrationality may, though, be ascribed if there is a clash between a particular belief or behavior and such background assumptions. Thus, a thorough-going physicalist may, perhaps, be accused of irrationality if she simultaneously believes in psychic powers. A theory of rationality cannot, therefore, be viewed as clarifying either what people should believe or how people should act—but it can determine whether beliefs and behaviors are compatible. Similarly, a theory of rational choice cannot determine whether it is rational to smoke or to exercise daily; but it might clarify whether a particular choice is compatible with other beliefs and choices.
From this viewpoint, normative theories can be viewed as clarifying conditions of consistency… Logic can be viewed as studying the notion of consistency over beliefs. Probability… studies consistency over degrees of belief. Rational choice theory studies the consistency of beliefs and values with choices.
They go on to clarify that by probability they mean Bayesian probability theory, and by rational choice theory they mean Bayesian decision theory. You'll get the same account in the textbooks on the cogsci of rationality, e.g. Thinking and Deciding or Rational Choice in an Uncertain World.