Er...I don't know why that website would use a well-established logical argument name in order to label something that is simply the straw man fallacy (or possibly the slippery-slope fallacy).
Reductio ad absurdum, as a term in logic, has never referred to a fallacy in any other text I have ever seen, not even in my 400-level logic courses.
Merriam-Webster and the
Collins dictionary both expressly state that it is a valid form of argument; the Internet Encyclopedia of Philosophy (which is written by accredited experts in the field, not user contributions like Wikipedia)
explicitly states that it has been used in mathematics and logic since antiquity. It is, for example, a common way to prove that there is no smallest rational number (that is, a number of the form "
A/B," where
A and
B are both integers), because any candidate you might pick can have its denominator
B doubled, generating a strictly smaller rational number, meaning we can derive the negation of the original assumption from the assumption itself.
Now, the burden on someone making a
reductio argument is that they must show (a) the absurd conclusion
does in fact necessarily follow, and (b) that the absurd conclusion is
relevant to the claims being made. But failing either of those doesn't make the
reductio ITSELF a fallacy; failing the former is simply the slippery-slope fallacy (the assertion that a chain of consequences is necessary when it is not), and failing the latter is the straw-man fallacy (pretending that the actual claim is a different, absurd claim instead).
Reductio ad absurdum itself is, and always has been, a perfectly valid logical form--as another example, Euclid used it to prove that there is no finite list containing all prime numbers. (Phrased as such because, at the time, they did not think of integers as we do, and were not comfortable with a concept like "infinity"; in practice, it
means the set of prime numbers is infinite, but the
reductio as used only denies the claim that any delimited list of primes is complete.)
You are correct that the "fallacy fallacy" is a problem, but not correct in that noting a fallacy in someone's argument
is a good reason to say they have the burden to update their argument. That is, it is an informal fallacy to assert, "Because the argument against my position was fallacious, my position is thus correct." This is not guaranteed; someone can easily use fallacious arguments in defense of true things, in fact it's quite common. However, the more restrained claim, "Your position remains undefended, because the defense provided was fallacious," is perfectly valid and is, in fact, the correct response to a fallacy: noting it and, all else being equal, permitting correction thereof, if correction can be made.