In the UK, this wording derives the Patents Act 1977 s 1(2), which provides (emphasis added):
It is hereby declared that the following (among other things) are not inventions for the purposes of this Act, that is to say, anything which consists of -
(a) a discovery, scientific theory or mathematical method;
(b) a literary, dramatic, musical or artistic work or any other aesthetic creation whatsoever;
(c) a scheme, rule or method for performing a mental act, playing a game or doing business, or a program for a computer;
(d) the presentation of information;
but the foregoing provision shall prevent anything from being treated as an invention for the purposes of this Act only to the extent that a patent or application for a patent relates to that thing as such.
In this context, the "as such" exclusion means that there must be something more to the invention than just a business method or a computer program. This might be controlling a machine, or improving the operation of a computer, or any number of other things. But there must be something more. This is quite tidily stated by MOPP s 1.35:
Therefore, a computer program that provides a technical contribution will not fall under the exclusion, as it is more than a computer program as such.
In determining whether an invention is excluded, the UKIPO applies the Aerotel test:
(1) Properly construe the claim;
(2) identify the actual contribution;
(3) ask whether it falls solely within the excluded subject matter;
(4) check whether the actual or alleged contribution is actually technical in nature.
The Aerotel test thus focuses on whether the actual contribution is excluded, rather than the claimed subject matter as a whole. Thus merely embodying a business method in a physical device is not enough to avoid it being excluded subject matter, if the physical device is just commonplace window dressing (such as a processor and memory).
Thus, that objection broadly means that the actual contribution falls solely into an excluded category with nothing further involved.
How to respond
In applying the Aerotel test, you will notice that the actual contribution must fall solely within the excluded subject matter. You may therefore want to characterise the actual contribution differently from the examiner. Or you may want to point to a facet of it that is not excluded.
An aside about that website
I would disagree with the editorialising of that website. Or more explicitly, that page is biased and uninformed twaddle. The words "as such" certainly reduce the scope of an exclusion, but do not render it meaningless. As you have noticed, the UKIPO readily object to excluded subject matter. And the EPO have no problem objecting to excluded subject matter (albeit sometimes through the mechanism of non-technical features not supporting an inventive step).